Abelian groups admitting fixed-point-free automorphisms of order $q^n$

S. V. Larin

Krasnoyarsk State Pedagogical University

Abstract: For a wide class of Abelian groups, necessary and sufficient conditions under which a group admits an automorphism of order $q^n$ are found; we also present necessary and sufficient conditions under which a group admits an automorphism $\varphi$ of order $q^n$ such that $\varphi^{qm}$ is a fixed-point-free automorphism for some $m<n$.

UDC: 519.4

Received: 09.03.1976

 English version: Mathematical Notes, 1977, 21:2, 132–137

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