《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 64-73.doi: 10.6040/j.issn.1671-9352.0.2021.565
• • 上一篇
韦萌萌1,李伟霞1*,邢建民2
WEI Meng-meng1, LI Wei-xia1*, XING Jian-min2
摘要： 利用射影特殊线性群PSL(2,2n)在射影直线X=GF(2n)∪{∞}的9-子集上的作用,通过计算具有固定长度的轨道的条数,给出了所有以PSL(2,2n)为自同构群、区组长度为9的单纯3-设计。
中图分类号:
| [1] BIGGS N L, WHITE A T. Permutation groups and combinatorial structures[M]. Cambridge: Cambridge University Press, 1979: 1-27. [2] CUSACK C A, GRAHAM S W, KREHER D L. Large sets of 3-designs from PSL(2,q)with block sizes 4 and 5[J]. Journal of Combinatorial Designs, 1995, 3(2):147-160. [3] OMIDI G R, POURNAKI M R, TAYFEH-REZAIE B. 3-designs with block size 6 from PSL(2,q)and their large sets[J]. Discrete Mathematics, 2007, 307(13):1580-1588. [4] CAMERON P J, MAIMANI H R, OMIDI G R, et al. 3-designs from PSL(2,q)[J]. Discrete Mathematics, 2006, 306(23):3063-3073. [5] KERANEN M S, KREHER D L, SHIUE P J S. The quadruple systems of the projective special linear group PSL(2,q)[J]. Journal of Combinatorial Designs, 2003, 11(5):339-351. [6] KERANEN M S, KREHER D L. 3-designs from PSL(2,2n)with block sizes 4 and 5[J]. Journal of Combinatorial Designs, 2004, 12(2):103-111. [7] LI Weixia, SHEN Hao. Simple 3-designs of PSL(2,2n)with block size 6[J]. Discrete Mathematics, 2008, 308(14):3061-3072. [8] LI Weixia, SHEN Hao. Simple 3-designs of PSL(2,2n)with block size 7[J]. Journal of Combinatorial Designs, 2008, 16(1):1-17. [9] GONG Luozhong, FAN Guobing. Simple 3-designs of PSL(2,2n)with block size 8[J]. Utilitas Mathematica, 2018, 106:3-9. [10] DICKSON L E. Linear groups, with an introduction to the Galois field theory[M]. New York: Dover Publications, 1958: 260-287. [11] TANG Jianxiong, LIU Weijun, WANG Jinhua. Groups PSL(n,q)and 3-(v,k,1)designs[J]. ARS Combinatoria, 2013, 110:217-226. |
| [1] | 海进科,李正兴. Sylow p-子群的结构对有限群的Coleman外自同构群的影响[J]. J4, 2013, 48(6): 5-8. |
|
||
