Abnormal subgroups and Carter subgroups in some infinite groups

2004/05/17 by Leonid A. Kurdachenko, L. A. Kurdachenko, Kurdachenko, L. A. +3
Mathematics · #20E34 #20F19 #20F22 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20E34 #msc:20F19 #msc:20F22

paper · pdf · doi:10.48550/arxiv.math/0405336

arxiv created 2004/05/17 · openalex publication_date 2004/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some properties of abnormal subgroups in generalized soluble groups will be considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it will be proven that a subgroup H of a radical group G is abnormal in G if and only if every intermediate subgroup for H coincides with its normalizer in G. This result will extend on radical groups the well-known criterion of abnormality for finite soluble groups obtained by D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugations will be also proven.

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