ON MINIMAL DEGREES OF PERMUTATION REPRESENTATIONS OF ABELIAN QUOTIENTS OF FINITE GROUPS

ON MINIMAL DEGREES OF PERMUTATION REPRESENTATIONS OF ABELIAN QUOTIENTS OF FINITE GROUPS

For a finite group G, we denote by μ(G) the minimum degree of a faithful permutation representation of G. We prove that if G is a finite p-group with an abelian maximal subgroup, then μ(G/G′)≤μ(G).

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2011-12, Vol.84 (3), p.408-413
1. Verfasser: FRANCHI, CLARA
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Permutations
Representations
Subgroups
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Zusammenfassung:For a finite group G, we denote by μ(G) the minimum degree of a faithful permutation representation of G. We prove that if G is a finite p-group with an abelian maximal subgroup, then μ(G/G′)≤μ(G).
ISSN:0004-9727
1755-1633
DOI:10.1017/S000497271100267X