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 (A) 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. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.