Locally finite Suzuki–Higman $2$-groups

N. M. Suchkov

Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660041 Russia

Abstract: We prove the following:
THEOREM. Let $U$ be a locally finite Suzuki–Higman $2$-group with respect to an automorphism group $H$. Then $U$ and $H$ are representable as the respective unions of ascending chains of finite subgroups
\begin{align*} U_1<U_2<&\dots<U_n<\dots,\\ H_1<H_2<&\dots<H_n<\dots, \end{align*}
in which case every subgroup $U_n$ is a Suzuki $2$-group with respect to $H_n$.

Keywords: locally finite Suzuki–Higman $2$-group, Suzuki $2$-group, automorphism group, ascending chain of finite subgroups.

UDC: 512.544

Received: 03.07.2016
Revised: 20.09.2016

DOI: 10.17377/alglog.2017.56.606

 English version: Algebra and Logic, 2018, 56:6, 479–497

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