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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.
Received: 03.07.2016 Revised: 20.09.2016
Citation:
N. M. Suchkov, “Locally finite Suzuki–Higman $2$-groups”, Algebra Logika, 56:6 (2017), 721–748; Algebra and Logic, 56:6 (2018), 479–497
Linking options:
https://www.mathnet.ru/eng/al827 https://www.mathnet.ru/eng/al/v56/i6/p721
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