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FINITE GROUPS WITH SOME ℨ-PERMUTABLE SUBGROUPS*

Published online by Cambridge University Press:  04 December 2009

YANGMING LI ,
LIFANG WANG  and
YANMING WANG
YANGMING LI
Affiliation:
Department of Mathematics, Guangdong Institute of Education, Guangzhou 510310, China e-mail: [email protected]
LIFANG WANG
Affiliation:
School of Mathematics and Computer, Shanxi Normal University, Linfen 041004, China e-mail: [email protected]
YANMING WANG
Affiliation:
Lingnan College and Department of Mathematics, Zhongshan University, Guangzhou 510275, China e-mail: [email protected]
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Abstract

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Let ℨ be a complete set of Sylow subgroups of a finite group G; that is to say for each prime p dividing the order of G, ℨ contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be ℨ-permutable in G if H permutes with every member of ℨ. In this paper we characterise the structure of finite groups G with the assumption that (1) all the subgroups of Gp ∈ ℨ are ℨ-permutable in G, for all prime p ∈ π(G), or (2) all the subgroups of Gp ∩ F*(G) are ℨ-permutable in G, for all Gp ∈ ℨ and p ∈ π(G), where F*(G) is the generalised Fitting subgroup of G.

Keywords

20D1020D20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 145 - 150
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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