Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-13T19:21:17.423Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite simple groups with nilpotent third maximal subgroups

Published online by Cambridge University Press:  09 April 2009

T. M. Gagen  and
Z. Janko
T. M. Gagen
Affiliation:
Australian National University, Canberra
Z. Janko
Affiliation:
Monash University, Melbourne
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.

We say that a subgroup H is an n-th maximal subgroup of G if there exists a chain of subgroups G = G0 > G1 > … > Gn = H such that each Gi is a maximal subgroup of Gi-1, i = 1, 2, …, n. The purpose of this note is to classify all finite simple groups with the property that every third maximal subgroup is nilpotent.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 4 , November 1966 , pp. 466 - 469
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Berkoviĉ, Ja. G., ‘The existence of subgroups of a finite non-soluble group’, Doki. A kad. Nauk 156 (1964), 1255–1257.Google Scholar
[2]Iwasawa, K., ‘Über die Struktur der endlichen Gruppen, deren echte Untergruppen sämtlich nilpotent sind’, Proc. Phys. Math. Soc. Japan 23 (1941), 1–4.Google Scholar
[3]Janko, Z., ‘Endliche Gruppen mit lauter nilpotenten zweitmaximalen Untergruppen’, Math. Zeitschr. 79 (1962), 422–424.CrossRefGoogle Scholar
[4]Miller, G. A., Blichfeldt, H. F. and Dickson, L. E., Theory and applications of finite groups (New York 1938).Google Scholar
[5]Suzuki, M., ‘On finite groups with cyclic Sylow subgroups for all odd primes’, Amer. J. Math. 77 (1955). 657–691.CrossRefGoogle Scholar
[6]Thompson, J. G., ‘Some simple groups’, Symposium on group theory (Harvard, 1963).Google Scholar