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THE SERIES OF NORMS IN A SOLUBLE p-GROUP

Published online by Cambridge University Press:  01 March 1997

R. A. BRYCE  and
JOHN COSSEY
R. A. BRYCE
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia
JOHN COSSEY
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia
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Abstract

The norm of a group G is the subgroup of elements of G which normalise every subgroup of G. We shall denote it κ(G). An ascending series of subgroups κi(G) in G may be defined recursively by: κ0(G) = 1 and, for i[ges ]0, κi+1(G)/κi(G) = κ(G/κi(G)). For each i, the section κi+1(G)/κi(G) clearly contains the centre of the group G/κi(G). A result of Schenkman [8] gives a very close connection between this norm series and the upper central series: ζi(G)⊆κi(G) ⊆ζ2i(G).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 165 - 172
Copyright
© The London Mathematical Society 1997

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