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Geometric coverings of groups and their directions

Published online by Cambridge University Press:  17 April 2009

Rolf Brandl
Rolf Brandl
Affiliation:
Mathematisches Institut, Am Hubland 12 D-8700 Würzburg West, Germany
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Abstract

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Let a group G be covered by finitely many disjoint cosets of subgroups Gi. We study conditions which imply that the subgroups Gi are conjugate in G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 177 - 184
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bloom, D.M., ‘The subgroups of PSL (3, q) for odd q’, Trans. Amer. Math. Soc. 127 (1967), 150–178.Google Scholar
[2]Blyth, R.D., ‘Rewriting products of group elements – I’, J. Algebra 116 (1988), 506–521.CrossRefGoogle Scholar
[3]Curzio, M., Longobardi, P., Maj, M. and Robinson, D.J.S., ‘A permutational property of groups’, Arch. Math. 44 (1985), 385–389.CrossRefGoogle Scholar
[4]Guralnick, R., ‘Subgroups of prime power index in a simple group’, J. Algebra 81 (1983), 304–311.CrossRefGoogle Scholar
[5]Guralnick, R., ‘Subgroups inducing the same permutation representation’, J. Algebra 81 (1983), 312–319.CrossRefGoogle Scholar
[6]Hestenes, M.D., ‘Singer groups’, Canad. J. Math. 22 (1970), 492–513.CrossRefGoogle Scholar
[7]Huppert, B., Endliche Gruppen I (Springer Verlag, Berlin-Heidelberg-New York, 1967).CrossRefGoogle Scholar
[8]Neumann, B.H., ‘Groups covered by permutable subsets’, J. London Math. Soc. 29 (1954), 236–248.CrossRefGoogle Scholar
[9]Parmenter, M.M., ‘Exact covering systems for groups’, Fund. Math. 123 (1984), 133–136.CrossRefGoogle Scholar
[10]Stammbach, U., ‘Cohomological characterisations of finite solvable and nilpotent groups’, J. Pwe Appl. Algebra 11 (1977/1978), 293–301.CrossRefGoogle Scholar
[11]Tomkinson, M.J., ‘FC-groups’, in Research Notes in Mathematics (Pitman, London, 1984).Google Scholar
[12]Zacher, G., ‘A lattice characterization ofthe index of a subgroup in a group’, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 69 (1980), 317–323.Google Scholar