Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T12:25:06.586Z Has data issue: false hasContentIssue false

Monomial representations and generalizations

Published online by Cambridge University Press:  09 April 2009

Christine Bessenrodt
Affiliation:
Fachbereich 11, Mathematik Lotharstrasse 65 D-4100 Duisburg Bundesrepublik Deutschland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the characteristic p analogue of M-groups, the so-called Mp-group Generalizing this notion, we also consider the condition that the modular irreducible representations are induced from representations of dimension < p, or even weaker, of dimension not divisible by p.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Burry, D. W. and Carlson, J. F., ‘Restrictions of modules to local subgroups’, Proc. Amer. Math. Soc. 84 (1982) 181184.CrossRefGoogle Scholar
[2]Dornhoff, L., Group representation theory, Part A (Marcel Dekker, New York, 1971).Google Scholar
[3]Dornhoff, L., ‘M-groups and 2-groupsMath. Z. 100 (1967) 226256.CrossRefGoogle Scholar
[4]Feit, W., The representation theory offinite groups (North-Holland, 1982).Google Scholar
[5]Gow, R., The p-subgroups of classical groups and some topics in the representation theory of soluble groups (Ph.D. Thesis, Liverpool, 1973).Google Scholar
[6]Huppert, B., Endliche Gruppen I (Springer, 1967).CrossRefGoogle Scholar
[7]Huppert, B. and Blackburn, N., Finite groups II (Springer, 1982).Google Scholar
[8]Huppert, B., ‘Gruppen mit modularer Sylowgruppe,’ Math. Z. 75 (1961), 140153.CrossRefGoogle Scholar
[9]Isaacs, I. M., ‘Generalizations of Taketa's theorem on the solvability of M-groups’, Proc. Amer. Math. Soc. 91 (1984), 192194.Google Scholar
[10]Knörr, R., ‘On the vertices of irreducible modules’, Ann. of Math. 110 (1979), 478499.CrossRefGoogle Scholar
[11]Michler, G. O., Brauer's conjectures and the classification offinite simple groups, (Springer Lecture Notes in Math. 1178, 1986, pp. 129142).Google Scholar
[12]Okuyama, T., ‘Module correspondence in finite groups,’ Hokkaido Math. J. 10 (1981), 299318.CrossRefGoogle Scholar
[13]Rigby, J. F., ‘Primitive linear groups containing a normal nilpotent subgroup larger than the centre of the group,’ J. London Math. Soc. 35 (1960), 389400.CrossRefGoogle Scholar
[14]Seitz, G. M. and Wright, C. R. B., ‘On finite groups whose Sylow subgroups are modular or quaternion-free,’ J. Algebra 13 (1969), 374381.CrossRefGoogle Scholar
[15]Seitz, G. M., ‘M-groups and the supersolvable residual,’ Math. Z. 110 (1969), 101122.CrossRefGoogle Scholar
[16]Tsushima, Y., ‘On the second reduction theorem of P. Fong,’ Kumamoto J. Sci. (Math.) 13 (1978), 15.Google Scholar
[17]van der Waall, R. W., ‘On monomial groups,’ J. Reine Angew. Math. 264 (1973), 103134.Google Scholar