A generalized Hughes property of finite groups.
A Hughes cover for exponent p (p a prime number) of a finite group is a union of subgroups whose (non-empty) complement consists of elements of order p. A proper Hughes subgroup is an instance of a Hughes cover; and its parent group is soluble by a well-known result of Hughes and Thompson. More generally an earlier result of the authors shows that a group with a Hughes cover of fewer than p subgroups is soluble. This article treats the insoluble groups having a Hughes cover for exponent p with...[Show more]
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|Source:||Communications in Algebra|
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