Yıl 2016,
Cilt: 3 Sayı: 3, 155 - 158, 09.08.2016
Öz
A finite cover $\mathcal{C}$ of a group $G$ is a finite collection of proper subgroups of $G$ such that $G$ is equal to the union of all of the members of $\mathcal{C}$. Such a cover is called {\em minimal} if it has the smallest cardinality among all finite covers of $G$. The covering number of $G$, denoted by $\sigma(G)$, is the number of subgroups in a minimal cover of $G$. In this paper the covering number of the Mathieu group $M_{24}$ is shown to be 3336.
Kaynakça
- W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24(3-4) (1997) 235–265.
- R. A. Bryce, V. Fedri, L. Serena, Subgroup coverings of some linear groups, Bull. Austral. Math. Soc. 60(2) (1999) 227–238.
- J. H. E. Cohn, On n-sum groups, Math. Scand. 75(1) (1994) 44–58.
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
- M. Epstein, S.S. Magliveras, D. Nikolova-Popova, The covering numbers of $A_9$ and $A_11$, to appear in the J. Combin. Math. Combin. Comput.
- P. E. Holmes, Subgroup coverings of some sporadic groups, J. Combin. Theory Ser. A 113(6) (2006) 1204–1213.
- L. C. Kappe, J. L. Redden, On the covering number of small alternating groups, Contemp. Math. 511 (2010) 109–125.
- L. C. Kappe, D. Nikolova-Popova, E. Swartz, On the covering number of small symmetric groups and some sporadic simple groups, arXiv:1409.2292v1 [math.GR].
- M. S. Lucido, On the covers of finite groups, in: C. M. Campbell, E. F. Robertson, G. C. Smith (Eds), Groups St. Andrews 2001, in Oxford, vol II, in : London Math. Soc. Lecture Note Ser. 305, 2003, 395–399.
- A. Maróti, Covering the symmetric groups with proper subgroups, J. Combin. Theory Ser. A 110(1) (2005) 97–111.
- M. J. Tomkinson, Groups as the union of proper subgroups, Math. Scand. 81(2) (1997) 191–198.
Yıl 2016,
Cilt: 3 Sayı: 3, 155 - 158, 09.08.2016
Öz
Kaynakça
- W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24(3-4) (1997) 235–265.
- R. A. Bryce, V. Fedri, L. Serena, Subgroup coverings of some linear groups, Bull. Austral. Math. Soc. 60(2) (1999) 227–238.
- J. H. E. Cohn, On n-sum groups, Math. Scand. 75(1) (1994) 44–58.
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
- M. Epstein, S.S. Magliveras, D. Nikolova-Popova, The covering numbers of $A_9$ and $A_11$, to appear in the J. Combin. Math. Combin. Comput.
- P. E. Holmes, Subgroup coverings of some sporadic groups, J. Combin. Theory Ser. A 113(6) (2006) 1204–1213.
- L. C. Kappe, J. L. Redden, On the covering number of small alternating groups, Contemp. Math. 511 (2010) 109–125.
- L. C. Kappe, D. Nikolova-Popova, E. Swartz, On the covering number of small symmetric groups and some sporadic simple groups, arXiv:1409.2292v1 [math.GR].
- M. S. Lucido, On the covers of finite groups, in: C. M. Campbell, E. F. Robertson, G. C. Smith (Eds), Groups St. Andrews 2001, in Oxford, vol II, in : London Math. Soc. Lecture Note Ser. 305, 2003, 395–399.
- A. Maróti, Covering the symmetric groups with proper subgroups, J. Combin. Theory Ser. A 110(1) (2005) 97–111.
- M. J. Tomkinson, Groups as the union of proper subgroups, Math. Scand. 81(2) (1997) 191–198.
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Yazarlar | |
|---|---|
| Yayımlanma Tarihi | 9 Ağustos 2016 |
| DOI | https://doi.org/10.13069/jacodesmath.90728 |
| IZ | https://izlik.org/JA46NH26KB |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 3 Sayı: 3 |