Vol. 41, No. 2, 1972

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On p-thetic groups

David Lee Armacost and William Louis Armacost

Vol. 41 (1972), No. 2, 295–301

The subject of this paper is a class of locally compact abelian (LCA) groups. Let p be a prime and let Z(p) denote the group of complex pn-th roots of unity equipped with the discrete topology. An LCA group G is called p-thetic if it contains a dense subgroup algebraically isomorphic to Z(p). It is shown that a p-thetic LCA group is either compact or is topologically isomorphic to Z(p). This fact leads to the formulation of a property which characterizes the p-thetic, the monothetic, and the solenoidal groups. Applications to some purely algebraic questions are presented.

Mathematical Subject Classification 2000
Primary: 22B05
Received: 25 February 1971
Published: 1 May 1972
David Lee Armacost
William Louis Armacost