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- 2017
可以表示成3个或4个交换子群并的群
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Abstract:
主要证明了一个群如果可以表示为3个或4个交换子群的并，则下列结论成立：① 群G可以表示成3个交换子群的并当且仅当G/Z(G)？Z2×Z2；② 群G可以表示成4个交换子群的并当且仅当G/Z(G)？S3或G/Z(G)？Z3×Z3.
This paper investigates the groups which are the unions of three or four abelian subgroups and obtains the following results: (1) Group G is the union of three abelian subgroups if and only if G/Z(G)？Z2×Z2; (2) Group G is the union of four abelian subgroups if and only if G/Z(G)？S3 or G/Z(G)？Z3×Z3
| [1] | 徐明耀. 有限群论导引[M]. 北京: 科学出版社, 2001. |
| [2] | AZAD A, IRANMANESH M A, PRAEGER C E. Abelian Coverings of Finite General Linear Groups and An Application to Their Non-Commuting Graphs[J]. J Algebraic Combin, 2011, 34: 683-710. DOI:10.1007/s10801-011-0288-2 |
| [3] | MASON D R. On Covering of A Finite Group by Abelian Subgroups[J]. Math Proc Camb Phil Soc, 1978, 83(2): 205-209. DOI:10.1017/S0305004100054463 |
| [4] | 宋科研, 晏燕雄. 论能表为四个真子群的并的群[J]. 西南大学学报(自然科学版), 2011, 33(2): 6-7. |
| [5] | 宋科研, 陈贵云. 再论能表示为三个交换子群的并的群[J]. 西南大学学报(自然科学版), 2009, 31(4): 6-7. |
