Result: On minimal faithful permutation representations of finite groups
Title:
On minimal faithful permutation representations of finite groups
Authors:
Source:
Bulletin of the Australian Mathematical Society. 62:311-317
Publisher Information:
Cambridge University Press (CUP), 2000.
Publication Year:
2000
Subject Terms:
Subgroups of symmetric groups, normal subgroups, quotient groups, Cayley's theorem, Finite nilpotent groups, \(p\)-groups, permutation representations, General theory for finite permutation groups, 0101 mathematics, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups, finite groups, factor groups
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1755-1633
0004-9727
0004-9727
DOI:
10.1017/s0004972700018797
Access URL:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7EBD744BD57C78D2CCB68175421B4E1D/S0004972700018797a.pdf/div-class-title-on-minimal-faithful-permutation-representations-of-finite-groups-div.pdf
https://digitalcollections.anu.edu.au/handle/1885/89268
http://www.journals.cambridge.org/abstract_S0004972700027489
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/on-minimal-faithful-permutation-representations-of-finite-groups/0C55A2C207214D2BFE4768F1D11B9EA0
https://openresearch-repository.anu.edu.au/handle/1885/89268
https://digitalcollections.anu.edu.au/handle/1885/89268
http://www.journals.cambridge.org/abstract_S0004972700027489
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/on-minimal-faithful-permutation-representations-of-finite-groups/0C55A2C207214D2BFE4768F1D11B9EA0
https://openresearch-repository.anu.edu.au/handle/1885/89268
Rights:
Cambridge Core User Agreement
Accession Number:
edsair.doi.dedup.....f12baa615b1890aa18c1d6c36ffb1b7c
Database:
OpenAIRE
Further Information
The minimal faithful permutation degree μ(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let N be a normal subgroup of a finite group G. We prove that μ(G/N) ≤ μ(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate the structure of a (hypothetical) minimal counterexample to this conjecture.