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RESEARCH ARTICLE
On growth of generalized Grigorchuk's overgroups
S. T. Samarakoon Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, TX 77843-3368, United States
Abstract:
Grigorchuk's Overgroup ˜G, is a branch group of intermediate growth. It contains the first Grigorchuk's torsion group G of intermediate growth constructed in 1980, but also has elements of infinite order. Its growth is substantially greater than the growth of G. The group G, corresponding to the sequence (012)∞=012012⋯, is a member of the family {Gω|ω∈Ω={0,1,2}N} consisting of groups of intermediate growth when sequence ω is not eventually constant. Following this construction, we define the family {˜Gω,ω∈Ω} of generalized overgroups. Then ˜G=˜G(012)∞ and Gω is a subgroup of ˜Gω for each ω∈Ω. We prove, if ω is eventually constant, then ˜Gω is of polynomial growth and if ω is not eventually constant, then ˜Gω is of intermediate growth.
Keywords:
growth of groups, intermediate growth, Grigorchuk group, growth bounds.
Received: 06.09.2019 Revised: 30.06.2020
Citation:
S. T. Samarakoon, “On growth of generalized Grigorchuk's overgroups”, Algebra Discrete Math., 30:1 (2020), 97–117
Linking options:
https://www.mathnet.ru/eng/adm768 https://www.mathnet.ru/eng/adm/v30/i1/p97
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Abstract page: | 89 | Full-text PDF : | 36 | References: | 32 |
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