AN ALGEBRAICALLY CLOSED GROUPS
https://doi.org/10.22405/2226-8383-2013-14-3-49-51
Abstract
Establish the solubility in any algebraically closed group G of each equation of the form w(x1, . . . , xn) = g, where w(x1, . . . , xn) – nonempty irreducible group word unknown x1, ...., xn, and g – arbitrary element of group G.
About the Authors
V. G. Durnev
Ярославский государственный университет им. П. Г. Демидова
Russian Federation
Russian Federation
O. V. Zetkina
Ярославский государственный университет им. П. Г. Демидова
Russian Federation
Russian Federation
A. I. Zetkina
Ярославский государственный университет им. П. Г. Демидова
Russian Federation
Russian Federation
References
1. Scott W. R. Algebraically closed groups // Proc. Amer. Math. Soc. 1951. Vol. 2. P. 118—121.
2. Neumann B. H. A note on algebraically closed groups // J. London. Math. Soc. 1952. Vol. 27. P. 227—242.
3. Macintyre A. On algebraically closed groups // Ann. of Math. 1972. Vol. 96. P. 53—97.
4. Линдон Р., Шупп П. Комбинаторная теория групп. М.: Мир, 1980.
Review
For citations:
Durnev V.G., Zetkina O.V., Zetkina A.I. AN ALGEBRAICALLY CLOSED GROUPS. Chebyshevskii Sbornik. 2013;14(3):49-51. (In Russ.) https://doi.org/10.22405/2226-8383-2013-14-3-49-51
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