A new efficient presentation for P S L ( 2 , 5 ) and the structure of the groups G ( 3 , m , n )

Bilal Vatansever; David M. Gill; Nuran Eren

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 1, page 67-74
  • ISSN: 0011-4642

Abstract

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G ( 3 , m , n ) is the group presented by 〈 a , b ∣ a 5 = ( a b ) 2 = b m + 3 a - n b m a - n = 1 〉 . 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 P S L ( 2 , 5 ) and in particular we prove that P S L ( 2 , 5 ) is isomorphic to G ( 3 , m , n ) under certain conditions.

How to cite

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Vatansever, Bilal, Gill, David M., and Eren, Nuran. "A new efficient presentation for $PSL(2,5)$ and the structure of the groups $G(3,m,n)$." Czechoslovak Mathematical Journal 50.1 (2000): 67-74. <http://eudml.org/doc/30542>.

@article{Vatansever2000,
abstract = {$G(3,m,n)$ 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.},
author = {Vatansever, Bilal, Gill, David M., Eren, Nuran},
journal = {Czechoslovak Mathematical Journal},
keywords = {special linear groups; finite groups; Schur multipliers; CAYLEY; efficient presentations},
language = {eng},
number = {1},
pages = {67-74},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new efficient presentation for $PSL(2,5)$ and the structure of the groups $G(3,m,n)$},
url = {http://eudml.org/doc/30542},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Vatansever, Bilal
AU - Gill, David M.
AU - Eren, Nuran
TI - A new efficient presentation for $PSL(2,5)$ and the structure of the groups $G(3,m,n)$
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 67
EP - 74
AB - $G(3,m,n)$ 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.
LA - eng
KW - special linear groups; finite groups; Schur multipliers; CAYLEY; efficient presentations
UR - http://eudml.org/doc/30542
ER -

References

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  9. Certain Classes of Group Presentations, Ph.D. thesis University of St. Andrews, 1992. (1992) 
  10. A new efficient presentation for P S L ( 2 , 13 ) and the structure of the groups G ( 7 , m ) , Doga-Tr. J. of Mathematics 17 (1993), 148–154. (1993) MR1226568
  11. A new efficient presentation for P S L ( 2 , 37 ) and the structure of the groups G ( 9 , m ) , J. Inst. Math. Comput. Sci. Math. Ser. 7 (1994), 207–211. (1994) MR1338491
  12. 10.1007/BF00052109, Acta Math. Hungar. 71 (1996), 205–210. (1996) MR1397552DOI10.1007/BF00052109
  13. The Deficiency of Finite Groups, Ph.D. thesis University of Queensland, 1968. (1968) 
  14. 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. (1982) Zbl0502.20003MR0679156

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