A finitely generated group G acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (GBS group). Such an action is described by a labeled graph. One GBS group can be presented by many labeled graphs. We study the embedding problem for GBS groups: to determine algorithmically when two given labeled graphs 𝔸1 and 𝔸2 define GBS groups G1 and G2 such that G1 is embeddable into G2. We prove that if G1 can be presented by only a finite number of reduced labeled graphs, then the embedding problem is solvable. Moreover, we describe the algorithm in this situation.
Funding source: RFBR
Award Identifier / Grant number: 14-01-90013-Bel_a
The author is grateful to V. A. Churkin for valuable comments and advice.
© 2015 by De Gruyter