INVARIANT FUNCTIONS ON FREE GROUPS AND SPECIAL HNN-EXTENSIONS
https://doi.org/10.22405/2226-8383-2017-18-1-109-122
Abstract
In this paper we are considering questions about the possibility of existence of invariant nontrivial pseudocharacters on free groups. It is proved that nontrivial pseudocharacters exist on a certain type of HNN-expansions in complex cases. We got some results about the width of verbal subgroups generated by words from commutator subgroup and non-triviality of the second group of bounded cohomologies for considered HNN-expansions. Thus, partial answer to the question, formulated R. I. Grigorchuk, is received. Pseudocharacter is the real functions f from group G to R such that f(xy)-f(x)-f(y) for some " > 0 and for any x; y 2 G and f(xn) = nf(x) 8n 2 Z, 8x 2 G. A pseudocharacter is called non-trivial if '(ab)
About the Author
D. Z. Kagan
Moscow University of Railway Engineering
Russian Federation
Russian Federation
Associate Professor, Ph. D. of mathematics, the department of Mathematics
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Review
For citations:
Kagan D.Z. INVARIANT FUNCTIONS ON FREE GROUPS AND SPECIAL HNN-EXTENSIONS. Chebyshevskii Sbornik. 2017;18(1):109-122. (In Russ.) https://doi.org/10.22405/2226-8383-2017-18-1-109-122
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