Finite permutation groups with large abelian quotients

László Kovács, Cheryl E. Praeger

Type: Article

Publication Date: 1989-02-01

Citations: 37

DOI: https://doi.org/10.2140/pjm.1989.136.283

Abstract

We show that if G is a group of permutations on a set of n points and if \G/G'\ denotes the order of its largest abelian quotient, then either \G/G'\ = 1 or there is a prime p dividing \G/G'\ such that \G/G'\ < p n/p .Equality holds if and only if G is a p-group which is the direct product of its transitive constituents, with each of those having order /?, except when p = 2 in which case one must also allow as transitive constituents the groups of order 4, the dihedral group of order 8 and degree 4, and the extraspecial group of order 32 and degree 8.

Locations

Pacific Journal of Mathematics - View - PDF
Project Euclid (Cornell University) - View - PDF

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