Boschheidgen, Jan, Klopsch, Benjamin and Thillaisundaram, Anitha (2020) Generating pairs of projective special linear groups that fail to lift. Mathematische Nachrichten, 293 (7). pp. 12511258. ISSN 0025584X
Full content URL: https://doi.org/10.1002/mana.201900354
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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 ntuple of H, a homomorphism from G to H, and a generating ntuple 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 
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ID Code:  36795 
Deposited On:  18 Sep 2019 07:59 
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