A characteristic subgroup of a group of odd order

Z. Arad; G. Glauberman

doi:10.2140/pjm.1975.56.305

A characteristic subgroup of a group of odd order

Z. Arad
, G. Glauberman

Tel Aviv University
The University of Chicago

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

Let G be a finite solvable group of odd order. Suppose p is a prime, S is a Sylow p-subgroup of G, and O_p (G) = 1. Let J(S) be the Thompson subgroup of S. Then, by a result of the second author (Lemma 6), Z(J(S)) <3 G.The object of this paper is to generalize the above result by replacing the prime p by a set of primes π.

Original language	English
Pages (from-to)	305-319
Number of pages	15
Journal	Pacific Journal of Mathematics
Volume	56
Issue number	2
DOIs	https://doi.org/10.2140/pjm.1975.56.305
State	Published - Feb 1975
Externally published	Yes

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title = "A characteristic subgroup of a group of odd order",

abstract = "Let G be a finite solvable group of odd order. Suppose p is a prime, S is a Sylow p-subgroup of G, and Op (G) = 1. Let J(S) be the Thompson subgroup of S. Then, by a result of the second author (Lemma 6), Z(J(S)) <3 G.The object of this paper is to generalize the above result by replacing the prime p by a set of primes π.",

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N2 - Let G be a finite solvable group of odd order. Suppose p is a prime, S is a Sylow p-subgroup of G, and Op (G) = 1. Let J(S) be the Thompson subgroup of S. Then, by a result of the second author (Lemma 6), Z(J(S)) <3 G.The object of this paper is to generalize the above result by replacing the prime p by a set of primes π.

AB - Let G be a finite solvable group of odd order. Suppose p is a prime, S is a Sylow p-subgroup of G, and Op (G) = 1. Let J(S) be the Thompson subgroup of S. Then, by a result of the second author (Lemma 6), Z(J(S)) <3 G.The object of this paper is to generalize the above result by replacing the prime p by a set of primes π.

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A characteristic subgroup of a group of odd order

Abstract

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