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- 2018
亚循环群到亚循环群之间的同态个数
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Abstract:
摘要: 计算了一类m阶循环群通过2p阶循环群扩张的亚循环群之间的同态个数, 并给出了此类亚循环群自同态半群的阶。作为应用,验证了T. Asai和T. Yohsdia猜想对此类亚循环群成立。
Abstract: The number of homomorphisms between a class of metacyclic groups, which are normal cyclic groups of the order m extended by cyclic groups of the order 2p, is calculated, and the number of endomorphisms of such groups is obtained. As an application, the number of homomorphisms of such groups satisfies the conjecture of T.Asai and T.Yohsdia is varified
[1] | JOHNSON J. The number of group homomorphisms from <i>D<sub>m</sub></i> into <i>D<sub>n</sub></i>[J]. The College Mathematics Journal, 2013, 44:190-192. |
[2] | RAJKUMAR R, GAYATHRI M, ANITHA T. The number of homomorphisms from dihedral groups in to some finite groups[J]. Mathematical Sciences International Research Journal, 2015(4):161-165. |
[3] | 徐明曜. 有限群导引[M]. 北京:科学出版社,1999. XU Mingyao. Finite groups: an introduction[M]. Beijing: Science Press, 1999. |
[4] | BATE M. The number of homomorphisms from finite groups to classical groups[J]. J Algebra, 2007, 308:612-628. |
[5] | 闵嗣鹤,严士健. 初等数论[M]. 北京:高等教育出版社,2006. MIN Sihe, YAN Shijian. Elementary number theory[M]. Beijing: Higher Education Press, 2006. |
[6] | YOHSDIA T. Hom(<i>A,G</i>)(I)[J]. J Algebra, 1993, 156:125-156. |
[7] | RAJKUMAR R, GAYATHRI M, ANITHA T. Enumeration of homomorphisms from modular group in to some finite groups[J]. International Journal of Mathematics and Its Applications, 2015, 3(3B):15-19. |
[8] | ASAI T, YOHSDIA T. Hom(<i>A,G</i>)(II)[J]. J Algebra, 1993, 160:273-285. |