On groups with a strongly embedded unitary subgroup

2020/04/29 by Anatoliy Sozutov, Sozutov, Anatoliy
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.2004.14216

8 pages, in Russian

arxiv created 2020/04/29 · arxiv updated 2020/04/30

Abstract

The proper subgroup B of the group G is called \it strongly embedded, if 2∈π(B) and 2∉π(B ∩ B^g) for any element g ∈ G ∖ B and, therefore, N_G(X) ≤ B for any 2-subgroup X ≤ B . An element a of a group G is called \it finite if for all g∈ G the subgroups ⟨ a, a^g ⟩ are finite. In the paper, it is proved that the group with finite element of order 4 and strongly embedded subgroup isomorphic to the Borel subgroup of U₃(Q) over a locally finite field Q of characteristic 2 is locally finite and isomorphic to the group U₃(Q). Keywords: A strongly embedded subgroup of a unitary type, subgroups of Borel, Cartan, involution, finite element.

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