P-dominated group

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The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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Definition

A finite group G is termed a p-dominated group for some prime p if it satisfies the following conditions:

  1. G is a finite complete group: in other words, G is complete: it is centerless and every automorphism of the group is inner.
  2. The Fitting subgroup F(G) is a p-group.
  3. The quotient G/F(G) is a p'-group (i.e., its order is relatively prime to p). In fact, G is a semidirect product of F(G) and a p'-group.

Facts