Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T01:13:52.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Index Four Simple Groups

Published online by Cambridge University Press:  20 November 2018

Leo J. Alex  and
Dean C. Morrow
Leo J. Alex
Affiliation:
State University College of New York, Oneonta, New York
Dean C. Morrow
Affiliation:
State University College of New York, Oneonta, New York
Rights & Permissions [Opens in a new window]

Extract

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.

An index four simple group is a finite simple group, G, with a self-centralizing Sylow p-subgroup whose normalizer in G has order 4p. In this paper index four simple groups having a non-principal ordinary irreducible character of small degree in the principal p-block are studied.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 1 - 21
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Alex, L. J., Index two simple groups, J. Algebra 31 (1974), 262–275.Google Scholar
2. Blichfeldt, H. L., Finite collineation groups (University of Chicago Press, Chicago, 1917).Google Scholar
3. Brauer, R., On simple groups of order 5 3a 2b, Bull. Amer. Math. Soc. 14 (1968), 900–903.Google Scholar
4. Brauer, R., On groups whose order contains a prime number to the first power, I, II, Amer. J. Math. 1942, 401–440.Google Scholar
5. Brauer, R. and Fowler, K. A., On groups of even order, Ann. of Math. 62 (1955), 565–583.Google Scholar
6. Brauer, R. and Tuan, H. F., On simple groups of finite order, Bull. Amer. Math. Soc. 51 (1945), 756–766.Google Scholar
7. Dornhoff, L., Group representation theory (Marcel Dekker, New York, 1971).Google Scholar
8. Feit, W., The current situation in the theory of finite simple groups, Yale University, New Haven, 1970.Google Scholar
9. Feit, W., On finite linear groups, J. Algebra 5 (1967), 378–400.Google Scholar
10. Glauberman, G., Central elements in core-free groups, J. Algebra 4 (1966), 403–420.Google Scholar
11. Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
12. Hall, M., Jr., Nonexistence of a finite group with a specified 7-block, Proceedings of the Conference on Finite Groups (Academic Press, New York, 1976), 409–423.Google Scholar
13. Lindsey, J. H. II, On a projective representation of the Hall-Janko group, Bull. Amer. Math. Soc. 74 (1968), 1094.Google Scholar
14. Parrott, D., On the Mathieu groups M22 and Mn, J. Aust. Math. Soc. 11 (1970), 69–82.Google Scholar
15. Schur, I., Über eine Klasse von endliche Gruppen linearer Substitutionen (Sitz der Preussichen Akad., Berlin, 1905), 87–91.Google Scholar
16. Stanton, R. G., The Mathieu groups, Can. J. Math. 3 (1951), 164–174.Google Scholar
17. Suzuki, M., Finite groups in which the centralizer of any element is 2-closed, Ann. Math. 82 (1965), 191–212.Google Scholar
18. Thompson, J. G., Finite groups with fixed-point-free automorphisms of prime order, Proc. Nat. Acad. Sci., 45 (1959), 578–581.Google Scholar
19. Wales, D., Simple groups of order 7 3a 2b, J. Algebra 16 (1970), 575–596.Google Scholar