On amalgams of periodic groups

Abstract

It is known that two groups with an amalgamated subgroup can be embedded in a group, and if the given groups are finite, the embedding group can be chosen finite. The present paper deals with the question how ‘finite’ can here be relaxed to ‘locally finite’, ‘of finite exponent’, or ‘periodic’. An example shows that two locally finite groups of finite exponent, with an amalgamated subgroup, may not be embeddable even in a periodic group. Conditions that ensure the possibility of such embeddings are then investigated. The principal tool is the ‘permutational product’ of groups that has recently been introduced into the investigation of other embedding problems.