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On Finite Groups with an Abelian Sylow Group

Published online by Cambridge University Press:  20 November 2018

Richard Brauer  and
Henry S. Leonard Jr.
Richard Brauer
Affiliation:
Harvard University
Henry S. Leonard Jr.
Affiliation:
Carnegie Institute of Technology
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We shall consider finite groups of order of g which satisfy the following condition:

(*) There exists a prime p dividing g such that if P ≠ 1 is an element of p-Sylow group ofthen the centralizer(P) of P incoincides with the centralizer() of in.

This assumption is satisfied for a number of important classes of groups. It also plays a role in discussing finite collineation groups in a given number of dimensions.

Of course (*) implies that is abelian. It is possible to obtain rather detailed information about the irreducible characters of groups in this class (§ 4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 436 - 450
Copyright
Copyright © Canadian Mathematical Society 1962

References

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