Vol. 55, No. 2, 1974

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Cyclic amalgamations of residually finite groups

Benny Dan Evans

Vol. 55 (1974), No. 2, 371–379

A group G is said to be residually finite if the intersection of the collection of all subgroups of finite index in G is the trivial group. This paper is concerned; with the following question. If A and B are residually finite groups, and if G is the generalized free product of A and B with a single cyclic subgroup amalgamated, then what conditions on A and B will insure that G is residually finite? The main result of this paper is that there exists a class C of residually finite groups which contains all free groups, polycylic groups, fundamental groups of 2-manifolds, and other common residually finite groups, and in addition C is closed under the operation of forming generalized free products with a single cyclic subgroup amalgamated.

Mathematical Subject Classification 2000
Primary: 20E25
Received: 7 August 1973
Revised: 4 February 1974
Published: 1 December 1974
Benny Dan Evans