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On the Rank of a p-Group of Class 2

Published online by Cambridge University Press:  20 November 2018

U. H. M. Webb
U. H. M. Webb*
Affiliation:
Department of Pure Mathematics Queen Mary College (University of London) Mile End Road London E1 4NS
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Abstract

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Let d(G) denote the minimal number of generators of the finite p-group G, r(G) the maximum over all subgroups H of G of d(H) and ra(G) the maximum over all abelian subgroups H of G of d(H). If G is of class two it is clear that

By considering properties of the stability number of graphs we construct examples which show that any value of r(G) within these bounds can occur.

Keywords

20D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 1 , 01 March 1983 , pp. 101 - 105
Copyright
Copyright © Canadian Mathematical Society 1983

References

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3. Patterson, A. R. (MacWilliams), The minimal number of generators for p' subgroups of GL(n, p), J. Algebra 32, (1974) 132-140.Google Scholar
4. Wehrfritz, B. A. F., The rank of a linear p-group; An apology, J. Lond. Math. Soc. (2), 21 (1980), 237-243.Google Scholar