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On p-groups whose maximal subgroups are isomorphic

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Avinoam Mann
Avinoam Mann
Affiliation:
Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
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Abstract

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We give an improved bound for the order of a p-group enjoying the title property. We also point out relations between the upper central series of a p-group and of its maximal subgroups.

Keywords

maximal subgroups of p-groups.

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 143 - 147
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Berkovich, Ya. G., ‘A generalization of theorems of Ph. Hall and Blackburn and an application to non-regular p-groups’, Math. USSR (lzv.) 5 (1971), 815–844.CrossRefGoogle Scholar
[2]Hermann, P. Z., ‘On finite p-groups with isomorphic maximal subgroups’, J. Austral. Math. Soc. (Series A) 48 (1990), 199–213.CrossRefGoogle Scholar
[3]Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).CrossRefGoogle Scholar