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The Frattini Subgroup of a p-Group

Published online by Cambridge University Press:  20 November 2018

P. L. Manley
P. L. Manley*
Affiliation:
University of Windsor
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We prove that the Frattini subgroups are trivial for finite groups whose orders are not divisible by squares of a prime.

If G is a group, we define its Frattini subgroup ϕ(G) as the intersection of all the maximal subgroups of G. An element x ∈ G is a nongenerator of G if whenever G = < X, x >, where X ⊆ G, then G = < X >.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 511 - 512
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Gorenstein, D., Finite groups. (Harper and Row, New York, 1968).Google Scholar