Independent generating sets and geometries for symmetric groups

Peter J. Cameron; Philippe Cara

doi:10.1016/S0021-8693(02)00550-1

Independent generating sets and geometries for symmetric groups

Peter J. Cameron^*, Philippe Cara

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Julius Whiston showed that the size of an independent generating set in the symmetric group S_n is at most n - 1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group S_n for n > 6.

Original language	English
Pages (from-to)	641-650
Number of pages	10
Journal	Journal of Algebra
Volume	258
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(02)00550-1
Publication status	Published - 15 Dec 2002

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title = "Independent generating sets and geometries for symmetric groups",

abstract = "Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n - 1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group Sn for n > 6.",

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T1 - Independent generating sets and geometries for symmetric groups

AU - Cameron, Peter J.

AU - Cara, Philippe

PY - 2002/12/15

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N2 - Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n - 1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group Sn for n > 6.

AB - Julius Whiston showed that the size of an independent generating set in the symmetric group Sn is at most n - 1. We determine all sets meeting this bound. We also give some general remarks on the maximum size of an independent generating set of a group and its relationship to coset geometries for the group. In particular, we determine all coset geometries of maximum rank for the symmetric group Sn for n > 6.

UR - https://www.scopus.com/pages/publications/0037115927

U2 - 10.1016/S0021-8693(02)00550-1

DO - 10.1016/S0021-8693(02)00550-1

M3 - Article

AN - SCOPUS:0037115927

SN - 0021-8693

VL - 258

SP - 641

EP - 650

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Independent generating sets and geometries for symmetric groups

Abstract

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