This article is cited in 3 papers

Residually finite $p$-groups of generalized free products of groups

D. N. Azarov

Ivanovo State University, 37 Ermaka str., Ivanovo, 153025 Russia

Abstract: Let $p$ be a prime number. Recall that a group $G$ is said to be a residually finite $p$-group if for every nonidentity element $a$ of $G$ there exists a homomorphism of the group $G$ onto some finite $p$-group such that the image of the element $a$ differs from unity. For the free product of two residually finite $p$-groups with amalgamated finite subgroups we obtain a necessary and sufficient condition to be a residually finite $p$-group. This result is a generalization of the similar Higman theorem proved for a free product of two finite $p$-groups with amalgamation.

Keywords: free product of groups with amalgamated subgroups, residually finite $p$-group.

UDC: 512.543

Received: 16.10.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:5, 1–6

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