| Title:
|
A new efficient presentation for $PSL(2,5)$ and the structure of the groups $G(3,m,n)$ (English) |
| Author:
|
Vatansever, Bilal |
| Author:
|
Gill, David M. |
| Author:
|
Eren, Nuran |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
67-74 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
$G(3,m,n)$ is the group presented by $\langle a,b\mid a^5=(ab)^2=b^{m+3}a^{-n}b^ma^{-n}=1\rangle $. In this paper, we study the structure of $G(3,m,n)$. We also give a new efficient presentation for the Projective Special Linear group $PSL(2,5)$ and in particular we prove that $PSL(2,5)$ is isomorphic to $G(3,m,n)$ under certain conditions. (English) |
| MSC:
|
20D06 |
| MSC:
|
20F05 |
| idZBL:
|
Zbl 1038.20021 |
| idMR:
|
MR1745460 |
| . |
| Date available:
|
2009-09-24T10:30:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127549 |
| . |
| Reference:
|
[1] F.R. Beyl and J. Tappe: Group Extensions.Presentations and the Schur Multiplicator. Lecture Notes in Mathematics 958, Springer-Verlag, Berlin, 1982. MR 0681287 |
| Reference:
|
[2] C. M. Campbell and E. F. Robertson: A deficiency zero presentation for ${\mathrm SL}(2,p)$.Bull. London Math. Soc. 12 (1980), 17–20. MR 0565476, 10.1112/blms/12.1.17 |
| Reference:
|
[3] J. J. Cannon: An introduction to the group language CAYLEY.Proc. Durham Symposium on Computational Group Theory, Academic Press, London, 1984, pp. 145–183. MR 0760656 |
| Reference:
|
[4] H. S. Coxeter: The binary polyhedral groups and other generalizations of the quaternion group.Duke Math. J. 7 (1940), 367–379. Zbl 0024.15002, MR 0003409 |
| Reference:
|
[5] B. Huppert: Endliche Gruppen I.Springer, Berlin, 1967. Zbl 0217.07201, MR 0224703 |
| Reference:
|
[6] G. Karpilovsky: The Schur Multiplier.Oxford University Press, Oxford, 1987. Zbl 0619.20001, MR 1200015 |
| Reference:
|
[7] I. Schur: Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen.J. Reine Angew. Math. 132 (1907), 85–137. |
| Reference:
|
[8] R. G. Swan: Minimal resolutions for finite groups.Topology 4 (1965), 193–208. Zbl 0146.04002, MR 0179234, 10.1016/0040-9383(65)90064-9 |
| Reference:
|
[9] B. Vatansever: Certain Classes of Group Presentations.Ph.D. thesis University of St. Andrews, 1992. |
| Reference:
|
[10] B. Vatansever and E. F. Robertson: A new efficient presentation for $PSL(2,13)$ and the structure of the groups $G(7,m)$.Doga-Tr. J. of Mathematics 17 (1993), 148–154. MR 1226568 |
| Reference:
|
[11] B. Vatansever: A new efficient presentation for $PSL(2,37)$ and the structure of the groups $G(9,m)$.J. Inst. Math. Comput. Sci. Math. Ser. 7 (1994), 207–211. MR 1338491 |
| Reference:
|
[12] B. Vatansever: New efficient presentations for $PSL(2,5)$ and $ SL(2,5)$; the structure of the groups $G(5,m)$ and $G(m,n,r)$.Acta Math. Hungar. 71 (1996), 205–210. MR 1397552, 10.1007/BF00052109 |
| Reference:
|
[13] J. W. Wamsley: The Deficiency of Finite Groups.Ph.D. thesis University of Queensland, 1968. |
| Reference:
|
[14] J. Wiegold: The Schur Multiplier.Groups (St. Andrews, 1981), C. M. Campbell and E. F. Robertson (eds.), LMS Lecture Notes, 71, Cambridge University Press, 1982, pp. 137–154. Zbl 0502.20003, MR 0679156 |
| . |
