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INFLUENCE OF STRONGLY CLOSED 2-SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS

Published online by Cambridge University Press:  10 March 2011

HUNG P. TONG-VIET
HUNG P. TONG-VIET*
Affiliation:
Department of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK e-mail: [email protected]
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Abstract

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Let H ≤ K be subgroups of a group G. We say that H is strongly closed in K with respect to G if whenever ag ∈ K, where a ∈ H, g ∈ G, then ag ∈ H. In this paper, we investigate the structure of a group G under the assumption that every subgroup of order 2m (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 Theory13(2) (2010), 267–276).

Keywords

Primary 20D20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 577 - 581
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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