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A converse to Lagrange's theorem

Published online by Cambridge University Press:  09 April 2009

T. R. Berger
T. R. Berger
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.
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Abstract

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An integer n >0 is called a CLT-number if any group of order n has subgroups of order d for every divisor d of n. The Set of CLT-numbers n is characterized by properties of the prime factorization of n. In addition, if G has order dividing a CLT-number then the structure of G/CG(U) is given where U is a chief factor of G. As a consequence, it is shown that G is solvable of Fitting height at most 3.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 291 - 313
Copyright
Copyright © Australian Mathematical Society 1978

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