Abstract.
In [6], Çevik defined necessary and sufficient conditions for the presentation of a central extension of a cyclic group by an ordinary group to be p-Cockcroft, where p is a prime or 0. In this paper, as a next step of this above result, we will define the p-Cockcroft property for the presentation of a central extension of an abelian group by any group. Finally, as an application of the main result, we will present an example.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
YG Baik SJ Pride (1997) ArticleTitleOn the efficiency of coxeter groups Bull London Math Soc 29 32–36 Occurrence Handle0882.20018 Occurrence Handle1416403
YG Baik J Harlander SJ Pride (1998) ArticleTitleThe geometry of group extensions J Group Theory 1 396–416 Occurrence Handle1660412
WA Bogley SJ Pride (1993) Calculating generators of π2 C Hog-Angeloni W Metzler A Sieradski (Eds) Two Dimensional Homotopy and Combinatorial Group Theory Univ Press Cambridge 157–188
R Brown J Huebschmann (1982) Identities among relations R Brown TL Thickstun (Eds) Low-Dimensional Topology SeriesTitleLondon Math Soc Lecture Note Series 48 Univ Press Cambridge 153–202
JH Conway HSM Coxeter GC Shephard (1972) ArticleTitleThe center of a finitely generated group Tensor 25 405–418 Occurrence Handle0236.20029 Occurrence Handle333001
AS Çevik (2001) ArticleTitleThe p-Cockcroft property of central extensions of groups Comm Algebra 29 1085–1094 Occurrence Handle0995.20014 Occurrence Handle10.1081/AGB-100001668 Occurrence Handle1842398
AS Çevik (2000) ArticleTitleThe efficiency of standard wreath product Proc Edinburgh Math Soc 43 415–423 Occurrence Handle0952.20021 Occurrence Handle1762899 Occurrence Handle10.1017/S0013091500021003
Dyer MN (1992) Cockroft 2-complexes. Preprint. University of Oregon
DBA Epstein (1961) ArticleTitleFinite presentations of groups and 3-manifolds Quart J Math Oxford 12 205–212 Occurrence Handle0231.55003 Occurrence Handle10.1093/qmath/12.1.205
SM Gersten (1987) Reducible diagrams and equations over groups SM Gersten (Eds) Essays in Group Theory Springer Berlin Heidelberg New York
ND Gilbert J Howie (1995) ArticleTitleThreshold subgroups for Cockcroft 2-complexes Comm Algebra 23 255–275 Occurrence Handle0872.57007 Occurrence Handle1311788
ND Gilbert J Howie (1994) ArticleTitleCockcroft properties of graphs of 2-complexes Proc Royal Soc Edinburgh, Sect A 124 363–369 Occurrence Handle0818.57003 Occurrence Handle1273754
J Harlander (1994) ArticleTitleMinimal cockcroft subgroups Glasgow J Math 36 87–90 Occurrence Handle0811.57010 Occurrence Handle1260822 Occurrence Handle10.1017/S0017089500030585
CW Kilgour SJ Pride (1996) ArticleTitleCockcroft presentations J Pure Appl Algebra 106 275–295 Occurrence Handle0851.20029 Occurrence Handle10.1016/0022-4049(95)00027-5 Occurrence Handle1375825
RC Lyndon PE Schupp (1977) Combinatorial Group Theory Springer Berlin Heidelberg New York Occurrence Handle0368.20023
SJ Pride (1991) Identities among relations of group presentations E Ghys A Haefliger A Verjovsky (Eds) Group Theory From A Geometrical Viewpoint, Tiresto 1990 World Scientific Singapore 687–717
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ateş, F., Sinan Çevik, A. The p-Cockcroft Property of Central Extensions of Groups II. Mh Math 150, 181–191 (2007). https://doi.org/10.1007/s00605-006-0435-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-006-0435-3