Automorphisms of higher rank lamplighter groups

作者：Stein Melanie^*; Taback Jennifer; Wong Peter

来源：International Journal of Algebra and Computation, 2015, 25(8): 1275-1299.

DOI：10.1142/S0218196715500411

• Diestel-Leader groups
• Diestel-Leader graphs
• automorphisms
• property R-infinity
• Reidemeister number
• twisted conjugacy classes

Let Gamma(d)(q) denote the group whose Cayley graph with respect to a particular generating set is the Diestel-Leader graph DLd(q), as described by Bartholdi, Neuhauser and Woess. We compute both Aut(Gamma(d)(q)) and Out(Gamma(d)(q)) for d >= 2, and apply our results to count twisted conjugacy classes in these groups when d >= 3. Specifically, we show that when d >= 3, the groups Gamma(d)(q) have property R-infinity, that is, every automorphism has an infinite number of twisted conjugacy classes. In contrast, when d = 2 the lamplighter groups Gamma(2)(q) = Lq = Z(q) Z have property R-infinity if and only if (q, 6) not equal 1.

• 出版日期2015-12