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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
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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

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References

REFERENCES

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