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Finite equilibrated groups

Published online by Cambridge University Press:  24 October 2008

Norman Blackburn ,
Marian Deaconescu  and
Avinoam Mann
Norman Blackburn
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL
Marian Deaconescu
Affiliation:
Faculty of Mathematics, University of Timisoara, Timisoara, Rumania
Avinoam Mann
Affiliation:
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Extract

If H, K are subgroups of a group G, then HK is a subgroup of G if and only if HK = KH. This condition certainly holds if H ≤ NG(K) or K ≤ NG(H). But the majority of groups can also be expressed as HK, where neither H nor K is normal. In this paper we consider groups G for which no subgroup G1 can be expressed as the product of non-normal subgroups of G1. Such a group is said to be equilibrated. Thus G is equilibrated if and only if either H ≤ NG(K) or K ≤ NG(H) whenever H, K and HK are subgroups of G.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 579 - 588
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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