Multiple Amalgamated Free Products and Multiple Free Products with Commuting Subgroups by Trees

Abstract

We define multiple amalgamated free product of groups
and multiple free product of groups with commuting subgroups and we prove that when a group G acts on a tree Γ such that the quotient graph G/Γ is pathn−1, G may
be identified with the free product of n groups (n integer
greater or equal to 2) with amalgamated subgroups and every free product of n groups with amalgamated subgroups
is obtained uniquely in this way. Finally we show a similar
characterization for a free product of n groups with commuting subgroups.
Math. Subject Classification: Primary 20E06; Secondary 05E18, 05C05, 05C25, 05C38.