Groups Saturated with Finite Frobenius Groups with Complements of Even Order

We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈 a ,  b g 〉, where g ∈ G, are finite, then G...

Full description

Saved in:
Bibliographic Details
Published in:Algebra and logic 2022, Vol.60 (6), p.375-379
Main Author: Durakov, B. E.
Format: Article
Language:English
Subjects:
Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Subgroups
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈 a ,  b g 〉, where g ∈ G, are finite, then G = A λ C G (i) is a Frobenius group with Abelian kernel A and complement C G (i) whose elementary Abelian subgroups are all cyclic.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-022-09664-0