2 results
Twisted Alexander ideals and the isomorphism problem for a family of parafree groups
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 63 / Issue 3 / August 2020
- Published online by Cambridge University Press:
- 22 June 2020, pp. 780-806
-
- Article
- Export citation
-
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 isomorphic. As a consequence, we solve the isomorphism problem for sub-families containing infinitely many groups Gi,j.
Applications of the Alexander Ideals to the Isomorphism Problem for Families of Groups
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 1 / February 2017
- Published online by Cambridge University Press:
- 19 May 2016, pp. 177-185
-
- Article
- Export citation
