Covering Groups of Rank 1 of Elementary Abelian Groups

ABSTRACT

Covering groups of elementary Abelian groups of odd exponent p can be classified according to the rank of their pth power homomorphisms, which may be regarded as linear transformations of 𝔽 _p –vector spaces. This article contains a description of the isomorphism types and the automorphism groups of those covering groups in which this rank is 1. Analogous considerations of elementary Abelian 2-groups and their covering groups are included in the final section.

Key Words:

• Automorphism
• Covering group
• Elementary Abelian

Mathematics Subject Classification:

• Primary 20D15
• Secondary 20D45

Notes

Communicated by A. Turull.