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Finite p-groups with Homogyclic Central Factors

Published online by Cambridge University Press:  20 November 2018

Joseph A. Gallian
Joseph A. Gallian*
Affiliation:
University of Minnesota, Duluth, Duluth, Minnesota
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If G has nilpotence class c(G) = c, let G = L1(G) > L2 (G)> . . . > Lc+1(G) = 1 and 1 = Z0(G) < Z1(G) < . . . < Zc(G) = G denote the lower central series and upper central series of G respectively. When there is no possibility of confusion we use Li for Li(G) and Zi for Zi(G). Throughout the paper we assume that G is a finite p-group of class greater than two. Let B (c, pr) denote the collection of all G of class c for which Li/Li+i is cyclic of order pr for i = 2, . . . , c and UC(c, pr) the collection of all G of class c for which Zi/Zi-1 is cyclic of order pr for i = 1, . . . , c – 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 636 - 643
Copyright
Copyright © Canadian Mathematical Society 1974

References

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