Generating pairs of projective special linear groups that fail to lift

Jan Boschheidgen, Benjamin Klopsch and Anitha Thillaisundaram

Mathematische Nachrichten, 2020, vol. 293, issue 7, 1251-1258

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 (h1,…,hn) of H, a homomorphism ϑ:G→H and a generating n‐tuple (g1,…,gn) of G such that (g1ϑ,…,gnϑ)=(h1,…,hn)? 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 Neumanns' problem. These new examples are easily described: G is a free product of two suitable finite cyclic groups, such as C2*C3, and H is a suitable finite projective special linear group, such as PSL(2,p) for a prime p≥5. A small modification yields the first negative examples (G,H) with H infinite.

Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201900354

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:293:y:2020:i:7:p:1251-1258

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().