Some special coprime actions and their consequences

Abstract

Let a group A act on the group G coprimely. Suppose that the order of the fixed point subgroup $C_G\left(A\right)$ is not divisible by an arbitrary but fixed prime p. In the present paper we determine bounds for the p-length of the group G in terms of the order of A, and investigate how some A-invariant p-subgroups are embedded in G under various additional assumptions.