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On connected transversals to Abelian subgroups

Published online by Cambridge University Press:  17 April 2009

Markku Niemenmaa  and
Tomas Kepka
Markku Niemenmaa
Affiliation:
Department of Mathematics, University of Oulu, SF-90570 Oulu, Finland
Tomas Kepka
Affiliation:
MFF - UK Prague, Czechoslovakia
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Abstract

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In this paper we investigate the situation where a group G has an abelian subgroup H with connected transversals. We show that if H is finite then G is solvable. We also investigate some special cases where the structure of H is very close to the structure of a cyclic group. Finally we apply our results to loop theory and we show that if the inner mapping group of a finite loop Q is abelian then Q is centrally nilpotent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 121 - 128
Copyright
Copyright © Australian Mathematical Society 1994

References

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