Vol. 23, No. 1, 1967

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On uniqueness of generalized direct decompositions

Francis C.Y. Tang

Vol. 23 (1967), No. 1, 171–182

Generalized direct products were introduced by B. H. Neuman and H. Neumann. In this paper we attempt to study some properties of generalized direct decompositions of groups. In general, decompositions of a given group into indecomposable generalized direct factors are not unique up to isomorphisms. The main result of this paper is that if the commutator subgroup of G is a cyclic p-group contained in the center Z(G) then any two generalized direct decompositions of G into indecomposable generalized direct factors with respect to its center Z(G) of G are isomorphic modulo Z(G).

Mathematical Subject Classification
Primary: 20.52
Received: 30 July 1966
Published: 1 October 1967
Francis C.Y. Tang