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Covering the symmetric groups with proper subgroups
- Source :
-
Journal of Combinatorial Theory - Series A . Apr2005, Vol. 110 Issue 1, p97-111. 15p. - Publication Year :
- 2005
-
Abstract
- Abstract: Let G be a group that is a set-theoretic union of finitely many proper subgroups. Cohn defined to be the least integer m such that G is the union of m proper subgroups. Tomkinson showed that can never be 7, and that it is always of the form (q a prime power) for solvable groups G. In this paper we give exact or asymptotic formulas for . In particular, we show that , while for alternating groups we find unless or 9. An application of this result is also given. [Copyright &y& Elsevier]
- Subjects :
- *PERMUTATIONS
*ALGEBRA
*COMBINATORICS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00973165
- Volume :
- 110
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Combinatorial Theory - Series A
- Publication Type :
- Academic Journal
- Accession number :
- 17613926
- Full Text :
- https://doi.org/10.1016/j.jcta.2004.10.003