Generating pairs of projective special linear groups that fail to lift
(2020) In Mathematische Nachrichten 293(7). p.1251-1258- Abstract
- The following problem was originally posed by B. H. Neumann and H. Neumann.Suppose that a group can be generated by elements and that is a homomor-phic image of . Does there exist, for every generating -tuple (ℎ1, … , ℎ ) of ,a homomorphism ∶ → and a generating -tuple (1, … , ) of such that( 1 , … , ) = (ℎ1, … , ℎ )?M. J. Dunwoody gave a negative answer to this question, by means of a carefullyengineered construction of an explicit pair of soluble groups. Via a new approach weproduce, for = 2, infinitely many pairs of groups (, ) that are negative examplesto Neumanns’ problem. These new examples are easily described: is a free productof two suitable finite cyclic groups, such as 2 ∗ 3, and is a suitable finite projec-tive... (More)
- The following problem was originally posed by B. H. Neumann and H. Neumann.Suppose that a group can be generated by elements and that is a homomor-phic image of . Does there exist, for every generating -tuple (ℎ1, … , ℎ ) of ,a homomorphism ∶ → and a generating -tuple (1, … , ) of such that( 1 , … , ) = (ℎ1, … , ℎ )?M. J. Dunwoody gave a negative answer to this question, by means of a carefullyengineered construction of an explicit pair of soluble groups. Via a new approach weproduce, for = 2, infinitely many pairs of groups (, ) that are negative examplesto Neumanns’ problem. These new examples are easily described: is a free productof two suitable finite cyclic groups, such as 2 ∗ 3, and is a suitable finite projec-tive special linear group, such as PSL(2, ) for a prime ≥ 5. A small modificationyields the first negative examples (, ) with infinite. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b89c2704-ef28-414d-8507-2ecab77c8851
- author
- Boschheidgen, Jan ; Klopsch, Benjamin and Thillaisundaram, Anitha LU
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematische Nachrichten
- volume
- 293
- issue
- 7
- pages
- 1251 - 1258
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:85084801337
- ISSN
- 1522-2616
- DOI
- 10.1002/mana.201900354
- language
- English
- LU publication?
- no
- id
- b89c2704-ef28-414d-8507-2ecab77c8851
- date added to LUP
- 2024-06-07 14:25:05
- date last changed
- 2024-08-07 10:07:32
@article{b89c2704-ef28-414d-8507-2ecab77c8851, abstract = {{The following problem was originally posed by B. H. Neumann and H. Neumann.Suppose that a group can be generated by elements and that is a homomor-phic image of . Does there exist, for every generating -tuple (ℎ1, … , ℎ ) of ,a homomorphism ∶ → and a generating -tuple (1, … , ) of such that( 1 , … , ) = (ℎ1, … , ℎ )?M. J. Dunwoody gave a negative answer to this question, by means of a carefullyengineered construction of an explicit pair of soluble groups. Via a new approach weproduce, for = 2, infinitely many pairs of groups (, ) that are negative examplesto Neumanns’ problem. These new examples are easily described: is a free productof two suitable finite cyclic groups, such as 2 ∗ 3, and is a suitable finite projec-tive special linear group, such as PSL(2, ) for a prime ≥ 5. A small modificationyields the first negative examples (, ) with infinite.}}, author = {{Boschheidgen, Jan and Klopsch, Benjamin and Thillaisundaram, Anitha}}, issn = {{1522-2616}}, language = {{eng}}, number = {{7}}, pages = {{1251--1258}}, publisher = {{John Wiley & Sons Inc.}}, series = {{Mathematische Nachrichten}}, title = {{Generating pairs of projective special linear groups that fail to lift}}, url = {{http://dx.doi.org/10.1002/mana.201900354}}, doi = {{10.1002/mana.201900354}}, volume = {{293}}, year = {{2020}}, }