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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cheb</journal-id><journal-title-group><journal-title xml:lang="ru">Чебышевский сборник</journal-title><trans-title-group xml:lang="en"><trans-title>Chebyshevskii Sbornik</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-8383</issn><publisher><publisher-name>Tula State Lev Tolstoy  Pedagogical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.22405/2226-8383-2019-20-2-391-398</article-id><article-id custom-type="elpub" pub-id-type="custom">cheb-650</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Краткие сообщения</subject></subj-group></article-categories><title-group><article-title>О дисперсивных по Оре F-гиперцентральных подгруппах конечных групп</article-title><trans-title-group xml:lang="en"><trans-title>On the F-hypercentral subgroups with the sylow tower property of finite groups</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мурашко</surname><given-names>Вячеслав Игоревич</given-names></name><name name-style="western" xml:lang="en"><surname>Murashka</surname><given-names>Viachaslau Igaravich</given-names></name></name-alternatives><email xlink:type="simple">mvimath@yandex.ru</email></contrib></contrib-group><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>28</day><month>01</month><year>2020</year></pub-date><volume>20</volume><issue>2</issue><fpage>391</fpage><lpage>398</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Мурашко В.И., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Мурашко В.И.</copyright-holder><copyright-holder xml:lang="en">Murashka V.I.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.chebsbornik.ru/jour/article/view/650">https://www.chebsbornik.ru/jour/article/view/650</self-uri><abstract><p>.</p></abstract><trans-abstract xml:lang="en"><p>.</p></trans-abstract></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Kaloujnine L. Über gewisse Beziehungen zwischen einer Gruppe und ihren Auto- morphismen // Berliner Mathematische Tagung, Berlin, 1953, P. 164–172.</mixed-citation><mixed-citation xml:lang="en">Kaloujnine L. 1953, “Über gewisse Beziehungen zwischen einer Gruppe und ihren Automorphismen”, Berliner Mathematische Tagung, Berlin, pp. 164–172.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Hall P. Some sufficient conditions for a group to be nilpotent // Illinois J. Math. 1958. V. 2, № 4. P. 787–801.</mixed-citation><mixed-citation xml:lang="en">Hall P. 1958, “Some sufficient conditions for a group to be nilpotent”, Illinois J. Math., vol. 2, no. 4, pp. 787–801.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Huppert B. Normalteiler und maximale Untergruppen endlicher Gruppen // Math. Z. 1954. V. 60, № 4. P. 409–434.</mixed-citation><mixed-citation xml:lang="en">Huppert B. 1954, “Normalteiler und maximale Untergruppen endlicher Gruppen”, Math. Z., vol. 60, no. 4, pp. 409–434.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Шеметков Л. А. Ступенчатые формации групп // Матем. сб. 1974. Т. 94(136), № 4(8), С. 628–648.</mixed-citation><mixed-citation xml:lang="en">Semetkov L. A. 1974, “Graduated formations of groups”, Mathematics of the USSR-Sbornik, vol. 23, no. 4, pp. 593–611.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Schmid P. Lokale Formationen endllcher Gruppen // Math. Z. 1974. V. 137, № 1. P. 31–48.</mixed-citation><mixed-citation xml:lang="en">Schmid P. 1974, “Lokale Formationen endllcher Gruppen”, Math. Z., vol. 137, no. 1, pp. 31–48. 6. Doerk K., Hawkes T. 1992, Finite soluble groups, Walter de Gruyter, Berlin–NewYork, 891 p.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Doerk K., Hawkes T. Finite soluble groups. Berlin–NewYork: Walter de Gruyter, 1992. 891 p.</mixed-citation><mixed-citation xml:lang="en">Hegarty P. V. 1994, “The absolute center of a group”, J. Algebra, vol. 169, pp. 929–935.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Hegarty P. V. The absolute center of a group // J. Algebra. 1994. V. 169. P. 929–935.</mixed-citation><mixed-citation xml:lang="en">Nasrabadi M. M., Gholamiam A. 2014, “On A-nilpotent abelian groups”, Proc. Indian Acad. Sci. (Math. Sci.), vol. 124, no. 4, pp. 517–525.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Nasrabadi M. M., Gholamiam A. On A-nilpotent abelian groups // Proc. Indian Acad. Sci. (Math. Sci.). 2014. V. 124, № 4. P. 517–525.</mixed-citation><mixed-citation xml:lang="en">Davoudirad S., Moghaddam M. R. R., Rostamyari M. A. 2016, “Autonilpotent groups and their properties”, Asian-European J. Math., vol. 9, no. 2, 1650056 (7 pages).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Davoudirad S., Moghaddam M. R. R., Rostamyari M. A. Autonilpotent groups and their properties // Asian-European J. Math. 2016. V. 9, № 2. 1650056 (7 pages).</mixed-citation><mixed-citation xml:lang="en">Hoseini S., Moghaddam M. R. R., Tajnia S. 2015, “On Auto-nipoltent groups”, Southeast Asian Bull. Math., vol. 39, pp. 219–224.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Hoseini S., Moghaddam M. R. R., Tajnia S. On Auto-nipoltent groups // Southeast Asian Bull. Math. 2015. V. 39. P. 219–224.</mixed-citation><mixed-citation xml:lang="en">Arora H., Karan R. 2018, “On Autonilpotent and Autosoluble Groups”, Note Mat., vol. 38, no. 1, pp. 35–45.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Arora H., Karan R. On Autonilpotent and Autosoluble Groups // Note Mat. 2018. V. 38, № 1. P. 35–45.</mixed-citation><mixed-citation xml:lang="en">Vasil’ev A. F., Vasil’eva T. I., Tyutyanov V. N. 2010, “On the finite groups of supersoluble type”, Sib. Math. J., vol. 51, no. 6, pp. 1004–1012.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Васильев А. Ф., Васильева Т. И., Тютянов В. Н. О конечных группах сверхразрешимого типа // Сиб. мат. журн. 2010. Т. 51, № 6. С. 1270–1281.</mixed-citation><mixed-citation xml:lang="en">Monakhov V. S., Kniahina V. N. 2013, “Finite groups with P-subnormal subgroups”, Ricerche mat., vol. 62, pp. 307–322.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Monakhov V. S., Kniahina V. N. Finite groups with P-subnormal subgroups // Ricerche mat. 2013. V. 62, P. 307–322.</mixed-citation><mixed-citation xml:lang="en">Zimmermann I. 1989, “Submodular subgroups in finite groups”, Math. Z., vol. 202, pp. 545–557.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Zimmermann I. Submodular subgroups in finite groups // Math. Z. 1989. V. 202. P. 545–557.</mixed-citation><mixed-citation xml:lang="en">Vasilyev V. A. 2015, “Finite groups with submodular Sylow subgroups”, Siberian Math. J., vol. 56, no. 6, pp. 1019–1027.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Васильев В. А. Конечные группы с субмодулярными силовскими подгруппами // Сиб. мат. журн. 2015. Т. 56, № 6. С. 1277–1288.</mixed-citation><mixed-citation xml:lang="en">Murashka V. I. 2018, “On analogues of Baer’s theorems for widely supersoluble hypercenter of finite groups”, Asian-European J. Math., vol. 11, no. 3, 1850043 (8 pages).</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Murashka V. I. On analogues of Baer’s theorems for widely supersoluble hypercenter of finite groups // Asian-European J. Math. 2018. V. 11, №. 3. 1850043 (8 pages).</mixed-citation><mixed-citation xml:lang="en">Murashka V. I. 2014, “Properties of the class of finite groups with P-subnormal cyclic primary subgroups”, Dokl. NAN Belarusi, vol. 58, no. 1, pp. 5–8. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Мурашко, В. И. Свойстав класса конечных групп с P-субнормальными циклическими примарными подгруппами // Докл. НАН Беларуси. 2014. Т. 58, № 1. С. 5–8.</mixed-citation><mixed-citation xml:lang="en">Baer R. 1959, “Supersoluble immersion”, Canad. J. Math., vol. 11, pp. 353–369.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Baer R. Supersoluble immersion // Canad. J. Math. 1959. V. 11. P. 353–369.</mixed-citation><mixed-citation xml:lang="en">Curran M. J. 1988, “Automorphisms of certain p-groups (p odd)”, Bull. Austral. Math. Soc., vol. 38, pp. 299-305.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Curran M. J. Automorphisms of certain p-groups (p odd) // Bull. Austral. Math. Soc. 1988. V. 38. P. 299–305.</mixed-citation><mixed-citation xml:lang="en">Groups, Algorithms, and Programming (GAP), Version 4.9.1 (2018). Available at http://www.gap-system.org (accessed 10 June 2018).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Groups, Algorithms, and Programming (GAP), Version 4.9.1. [Электронный ресурс] // URL: http://www.gap-system.org (дата обращения 10.06.2018).</mixed-citation><mixed-citation xml:lang="en">Baer R. 1953, “Group Elements of Prime Power Index”, Trans. Amer. Math Soc., vol. 75, no. 1, pp. 20–47.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Baer R. Group Elements of Prime Power Index // Trans. Amer. Math Soc. 1953. V. 75, № 1. P. 20–47.</mixed-citation><mixed-citation xml:lang="en">Isaacs I. M. 2008, Finite group theory, Graduate studies in mathematics, vol. 92, Providence, American Mathematical Society, 350 p.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Isaacs I. M. Finite group theory. Graduate studies in mathematics, V. 92. Providence: American Mathematical Society, 2008. 350 p.</mixed-citation><mixed-citation xml:lang="en">Skiba A. N. 2012, “On the F-hypercenter and the intersection of all F-maximal subgroups of a finite group”, J. Pure Appl. Algebra, vol. 216, no. 4, pp. 789–799.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Skiba A.N. On the F-hypercenter and the intersection of all F-maximal subgroups of a finite group // J. Pure Appl. Algebra. 2012. V. 216, № 4. P. 789–799.</mixed-citation><mixed-citation xml:lang="en">Shemetkov L. A. 1978, Formations of finite groups, Nauka, Moscow, 272 p. (In Russian)</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Шеметков Л. A. Формации конечных групп. М.: Наука, 1978. 272 с.</mixed-citation><mixed-citation xml:lang="en">Bidwell J. N. S., Curran M. J., McCaughan D. J. 2006, “Automorphisms of direct products of finite groups”, Arch. Math., vol. 86, pp. 481–489.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Bidwell J. N. S., Curran M. J., McCaughan D. J. Automorphisms of direct products of finite groups // Arch. Math. 2006. V. 86. P. 481–489.</mixed-citation><mixed-citation xml:lang="en">Bidwell J. N. S., Curran M. J., McCaughan D. J. Automorphisms of direct products of finite groups // Arch. Math. 2006. V. 86. P. 481–489.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
