Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-13T08:11:29.191Z Has data issue: false hasContentIssue false
  • English
  • Français

On centralizers of involutions in 2-groups

Published online by Cambridge University Press:  24 October 2008

Christian Ronse
Christian Ronse
Affiliation:
The Queen's College, Oxford
Get access Rights & Permissions [Opens in a new window]

Extract

1. Introduction. It is well known (see (5) and (6)) that if T is a 2-group containing an involution t such that |CT(t)| = 4, then T is dihedral, semidihedral or cyclic of order 4. Fomin(1) has studied 2-groups T containing an involution t such that |CT(t)| ≤ 8. He showed in particular that such a group has sectional 2-rank at most 4. In this paper we will prove the following:

Theorem A. Let T be a 2-group containing an involution t such that |CT(t)| ≤ 16. Then T has sectional 2-rank at most 6.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 199 - 204
Copyright
Copyright © Cambridge Philosophical Society 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Fomin, A. N.Finite 2-groups in which the centralizer of certain involution is of order 8. Ural. Gos. Univ. Mat. Zap. 8 (1972), no. 3, 122–132, 143(1973).Google Scholar
(2)Gorenstein, D.Finite Groups (Harper & Row, 1968).Google Scholar
(3)Liebeck, H. and Mchale, D.Groups with automorphisms inverting most elements. Math. Z. 124 (1972), 51–63.CrossRefGoogle Scholar
(4)Ronse, C. Finite permutation groups. Ph.D. Thesis, Oxford University (1979).Google Scholar
(5)Suzuki, M.A characterization of the simple groups LF(2, p), J. Fac. Sci. Univ. Tokyo 6, (1951) 259–293.Google Scholar
(6)Suzuki, M.On finite groups containing an element of order four which commutes only with its powers. Ill. J. Math. 3 (1959), 255–271.Google Scholar