Generating pairs of projective special linear groups that fail to lift

Boschheidgen, Jan and Klopsch, Benjamin and Thillaisundaram, Anitha (2020) Generating pairs of projective special linear groups that fail to lift. Mathematische Nachrichten . ISSN UNSPECIFIED

Documents
Generating pairs of projective special linear groups that fail to lift
Accepted Manuscript

Request a copy
[img] PDF
Lifting_generators_v2.pdf - Whole Document
Restricted to Repository staff only

298kB
Item Type:Article
Item Status:Live Archive

Abstract

The following problem was originally posed by B. H. Neumann and H. Neumann. Suppose that a group G can be generated by n elements and that H is a homomorphic image of G. Does there exist, for every generating n-tuple of H, a homomorphism from G to H, and a generating n-tuple of G such that the the generating tuple of G gets mapped to the generating tuple of H?
M.J. Dunwoody gave a negative answer to this question, by means of a carefully engineered construction of an explicit pair of soluble groups. Via a new approach we produce, for n=2, infinitely many pairs of groups (G,H) that are negative examples to the Neumanns' problem. These new examples are easily described: G is a free product of two suitable finite cyclic groups, and H is a suitable finite projective special linear group. A small modification yields the first negative examples (G,H) with H infinite.

Keywords:generating tuples, free products, projective special linear groups
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
Related URLs:
ID Code:36795
Deposited On:18 Sep 2019 07:59

Repository Staff Only: item control page