Influence of strongly closed 2-subgroups on the structure of finite groups

2010/05/24 by Hung P. Tong‐Viet, Hung P. Tong-Viet, Tong-Viet, Hung P.
Computer Science · Mathematics · #20D20 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20D20

paper · pdf · doi:10.48550/arxiv.1005.4284

6 pages

openalex publication_date 2010/05/24 · arxiv created 2011/02/24 · arxiv updated 2011/02/25 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let H≤ K be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever a^g ∈ K where a ∈ H, g ∈ G, then a^g ∈ H. In this paper, we investigate the structure of a group G under the assumption that every subgroup of order 2^m (and 4 if m = 1) of a 2- Sylow subgroup S of G is strongly closed in S with respect to G. Some results related to 2-nilpotence and supersolvability of a group G are obtained. This is a complement to Guo and Wei (J. Group Theory 13 (2010), no. 2, 267-276).

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