پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شماره‌ها | 1,674 |
| تعداد مقالات | 13,669 |
| تعداد مشاهده مقاله | 31,675,917 |
| تعداد دریافت فایل اصل مقاله | 12,511,528 |
All simple groups with order from 1 million to 5 million are efficient | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 3، شماره 1، خرداد 2014، صفحه 17-30 اصل مقاله (429.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2014.2984 | ||
| نویسندگان | ||
| Colin M. Campbell1؛ George Havas* 2؛ Colin Ramsay3؛ Edmund F. Robertson1 | ||
| 1School of Mathematics and Statistics, University of St Andrews | ||
| 2Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland | ||
| 3Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland | ||
| چکیده | ||
| There is much interest in finding short presentations for the finite simple groups. Indeed it has been suggested that all these groups are efficient in a technical sense. In previous papers we produced nice efficient presentations for all except one of the simple groups with order less than one million. Here we show that all simple groups with order between $1$ million and $5$ million are efficient by giving efficient presentations for all of them. Apart from some linear groups these results are all new. We also show that some covering groups and some larger simple groups are efficient. We make substantial use of systems for computational group theory and, in particular, of computer implementations of coset enumeration to find and verify our presentations. | ||
| کلیدواژه‌ها | ||
| Efficient presentations؛ simple groups؛ coset enumeration | ||
| مراجع | ||
|
W. Bosma, J. Cannon and C. Playoust (1997) The Magma
algebra system I: the user language J. Symbolic Comput., See also http://magma.maths.usyd.edu.au/magma/. 24, 235-265
J. N. Bray, M. D. E. Conder, C. R. Leedham-Green and E. A. O'Brien (2011) Short presentations for alternating and symmetric groups Trans. Amer. Math. Soc. 363, 3277-3285
C. M. Campbell, G. Havas, C. Ramsay and E. F.
Robertson (2004) Nice efficient presentations for all small simple groups and their covers LMS J. Comput. Math. 7, 266-283
C. M. Campbell, G. Havas, C. Ramsay and E. F.
Robertson (2007) On the efficiency of the simple groups with order less than a million and their covers Experiment. Math. 16, 347-358
C. M. Campbell and E. F. Robertson (1980) A deficiency zero
presentation for SL(2,p) Bull. London Math. Soc. 12, 17-20
C. M. Campbell and E. F. Robertson (1988) Computing with finite simple groups and their covering groups Computers in Algebra, ed. M. C. Tangora and M. Dekker, New
York , 17-26
C. M. Campbell, E. F. Robertson and P. D. Williams (1989) Efficient presentations for finite simple groups and related groups Groups-Korea 1988, Lecture Notes in Mathematics, 1398,
Springer, Berlin , 65-72
M. Conder, G. Havas and M. F. Newman (2011) On one-relator quotients of the modular group Groups St Andrews 2009 in Bath, Volume I,
London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge 387, 183-197
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson (1985) Atlas of finite groups Oxford University Press, Oxford
D. B. A. Epstein (1961) Finite presentations of groups and 3-manifolds Quart. J. Math. Oxford Ser. (2) 12, 205-212
The GAP~Group (2012) GAP -- Groups, Algorithms, and
Programming -- a System for Computational Discrete Algebra http://www.gap-system.org/
R. M. Guralnick, W. M. Kantor, M. Kassabov and A. Lubotzky (2008) Presentations of finite simple groups: a quantitative approach J. Amer. Math. Soc. 21, 711-774
R. M. Guralnick, W. M. Kantor, M. Kassabov and A. Lubotzky (2011) Presentations of finite simple groups: a computational approach J. Eur. Math. Soc. 13, 391-458
G. Havas and D. F. Holt (2010) On Coxeter's families of group presentations J. Algebra 324, 1076-1082
G. Havas and C. Ramsay (2001) Coset enumeration: ACE version 3.001 http://www.itee.uq.edu.au/~havas/ace3001.tar.gz
G. Havas and C. Ramsay (2003) Short balanced presentations of perfect groups Groups St Andrews 2001 in Oxford, Volume 1,
London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge 304, 238-243
G. Havas and C. Ramsay (2003) Breadth-first search and the Andrews-Curtis conjecture Internat. J. Algebra Comput. 13, 61-68
I. Korchagina and A. Lubotzky (2006) On presentations and second cohomology of some finite simple groups Publ. Math. Debrecen 69, 341-352
J. G.~Sunday (1972) Presentations of the groups SL(2,m) and PSL(2,m) Canad. J. Math. 24, 1129-1131
J. S. Wilson (2006) Finite axiomatization of finite
soluble groups J. London Math. Soc. (2) 74, 566-582
R. Wilson, P. Walsh, J. Tripp, Ibrahim Suleiman,
Richard Parker, Simon Norton, Simon Nickerson, Steve Linton, John Bray and Rachel Abbott (2012) ATLAS of Finite Group Representations - Version 3 http://brauer.maths.qmul.ac.uk/Atlas/v3/
| ||
|
آمار تعداد مشاهده مقاله: 5,212 تعداد دریافت فایل اصل مقاله: 3,151 |
||