Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:18:49.110Z Has data issue: false hasContentIssue false
  • English
  • Français

A classification of groups with a centralizer condition

Published online by Cambridge University Press:  17 April 2009

Zvi Arad  and
Marcel Herzog
Zvi Arad
Affiliation:
Department of Mathematics, Bar-IIan University, Ramat-Gan, Israel.
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.

Let G be a finite group. A nontrivial subgroup M of G is called a CC-subgroup if M contains the centralizer in G of each of its nonidentity elements. The purpose of this paper is to classify groups with a CC-subgroup of order divisible by 3. Simple groups satisfying that condition are completely determined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 1 , August 1976 , pp. 81 - 85
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Arad, Zvi, “A classification of 3CC-groups and applications to Glauberman-Goldschmidt theorem”, submitted.Google Scholar
[2]Feit, Walter and Thompson, John G., “Finite groups which contain a self-centralizing subgroup of order 3”, Nagoya Math. J. 21 (1962), 185–197.CrossRefGoogle Scholar
[3]Ferguson, Pamela A., “A theorem on CC subgroups”, J. Algebra 25 (1973), 203–221.CrossRefGoogle Scholar
[4]Ferguson, Pamela, “A classification for simple groups in terms of their Sylow 3 subgroups”, J. Algebra 33 (1975), 1–8.CrossRefGoogle Scholar
[5]Fletcher, L.R., “A characterisation of PSL(3, 4)”, J. Algebra 19 (1971), 274–281.CrossRefGoogle Scholar
[6]Goldschmidt, David M., “2-fusion in finite groups”, Ann. of Math. (2) 99 (1974), 70–117.CrossRefGoogle Scholar
[7]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[8]Gorenstein, Daniel, “Finite groups the centralizers of whose involutions have normal 2-complements”, Canad. J. Math. 21 (1969), 335–357.CrossRefGoogle Scholar
[9]Herzog, Marcel, “On finite groups which contain a Frobenius subgroup”, J. Algebra 6 (1967), 192–221.CrossRefGoogle Scholar
[10]Herzog, Marcel, “A characterization of some projective special linear groups”, J. Algebra 6 (1967), 305–308.CrossRefGoogle Scholar
[11]Stewart, W.B., “Groups having strongly self-centralizing 3-centralizers”, Proc. London Math. Soc. (3) 26 (1973), 653–680.CrossRefGoogle Scholar
[12]Suzuki, Michio, “Two characteristic properties of (ZT)-groups”, Osaka Math. J. 15 (1963), 143–150.Google Scholar