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A note on groups with non-central norm

Published online by Cambridge University Press:  18 May 2009

R. A. Bryce  and
L. J. Rylands
R. A. Bryce
Affiliation:
Department of Mathematics, Faculty of Science, Australian National University, Canberra Act 0200
L. J. Rylands
Affiliation:
Department of Mathematics, University of Western Sydney, Nepean, P.O. Box 10, Kingswood NSW 2747
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The norm K(G) of a group G is the subgroup of elements of G which normalize every subgroup of G. Under the name kern this subgroup was introduced by Baer [1]. The norm is Dedekindian in the sense that all its subgroups are normal. A theorem of Dedekind [5] describes the structure of such groups completely: if not abelian they are the direct product of a quaternion group of order eight and an abelian group with no element of order four. Baer [2] proves that a 2-group with non-abelian norm is equal to its norm.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 37 - 43
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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