Abstract:In 1969, Baumslag introduced a family of parafree groups Gi,j which share many properties with the free group of rank 2. The isomorphism problem for the family Gi,j is known to be difficult; a few small partial results have been found so far. In this paper, we compute the twisted Alexander ideals of the groups Gi,j associated with non-abelian representations into
$SL(2,{\mathbb Z}_2)$
. Using the twisted Alexander ideals, we prove that several pairs of groups among Gi,j are not isomo… Show more
“…Enumerating homomorphisms to finite groups was applied in [4,11], but could only deduce results for finitely many pairs (m, n). Recently, infinitely members in a subfamily of the G family have been distinguished from each other [9]. Results on the H family is rarely seen.…”
For any integers m, n with m = 0 and n > 0, let Gm,n denote the group presented by x, y, z | x = [z m , x][z n , y] ; for any integers m, n > 0, let Hm,n denote the group presented by x, y, z
“…Enumerating homomorphisms to finite groups was applied in [4,11], but could only deduce results for finitely many pairs (m, n). Recently, infinitely members in a subfamily of the G family have been distinguished from each other [9]. Results on the H family is rarely seen.…”
For any integers m, n with m = 0 and n > 0, let Gm,n denote the group presented by x, y, z | x = [z m , x][z n , y] ; for any integers m, n > 0, let Hm,n denote the group presented by x, y, z
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