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Elementary abelian operator groups

Published online by Cambridge University Press:  17 April 2009

Fletcher Gross
Fletcher Gross
Affiliation:
University of Utah, Salt Lake City, Utah, USA.
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Abstract

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Suppose G is a finite solvable p′-group admitting the elementary abelian p–group A as an operator group. if n = max{nilpotent length of CG(X)| X ∈ A#} and |A| ≥ pn+2, then the nilpotent length of G is n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 1 , August 1972 , pp. 91 - 100
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Carter, Roger and Hawkes, Trevor, “The F-normalizers of a finite soluble group”, J. Algebra 5 (1967), 175–202.CrossRefGoogle Scholar
[2]Feit, Walter and Thompson, John G., “Solvability of groups of odd order”, Pacific J. Math. 13 (1963), 775–1029.CrossRefGoogle Scholar
[3]Glauberman, George, “Fixed points in groups with operator groups”, Math. Z. 84 (1964), 120–125.CrossRefGoogle Scholar
[4]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[5]Gross, Fletcher, “A note on fixed-point-free solvable operator groups”, Proc. Amer. Math. Soc. 19 (1968), 1363–1365.CrossRefGoogle Scholar
[6]Hall, P. and Higman, Graham, “On the p–length of p–soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc. (3) 6 (1956), 1–42.CrossRefGoogle Scholar
[7]Shult, Ernest E., “On groups admitting fixed point free abelian operator groups”, Illinois J. Math. 9 (1965), 701–720.CrossRefGoogle Scholar
[8]Ward, J.N., “On finite groups admitting automorphisms with nilpotent fixed-point group”, Bull. Austral. Math. Soc. 5 (1971), 281–282.CrossRefGoogle Scholar
[9]Ward, J.N., “On finite soluble groups and the fixed-point groups of automorphisms”, Bull. Austral. Math. Soc. 5 (1971), 375–378.CrossRefGoogle Scholar