Product of some elements of finite groups

doi:10.1007/s11464-009-0043-3

Front. Math. China

2009, Vol. 4

Issue (4) : 739-747 https://doi.org/10.1007/s11464-009-0043-3

Research articles

Product of some elements of finite groups

Cui ZHANG¹,Wujie SHI²,

1.University of Primorska, FAMNIT, Glagoljaˇska 8, 6000 Koper, Slovenia；University of Primorska, PINT, Muzejski trg 2, 6000 Koper, Slovenia; 2.School of Mathematical Sciences, Suzhou University, Suzhou 215006, China;

Download: PDF(126 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract In this paper, some sufficient and necessary conditions for the commutative product of two elements of finite groups are given. Moreover, some results are obtained by investigating the product of some elements.

Keywords Element nilpotent solvable

Issue Date: 05 December 2009

Cite this article:

Cui ZHANG,Wujie SHI. Product of some elements of finite groups[J]. Front. Math. China, 2009, 4(4): 739-747.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0043-3
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I4/739

	Chen Z M. Inner and Outer-Σ-Groups and Minimal Non-Σ-Groups. Chongqing: Southwest Normal University Press, 1988 (in Chinese)
	Fan X Y. A note on the order of a product of commutative elements in a group. Journal of Capital Normal University, 2006, 4: 1―2, 6 (in Chinese)
	Foguel T. Conjugate-permutablesubgroups. J Algebra, 1997, 191: 235―239 doi: 10.1006/jabr.1996.6924
	Jie F Z. A result of the order of the product of finite order elements ina group. Journal of Central China NormalUniversity, 1988, 2: 139―140 (in Chinese)
	Kegel O H. Sylow grouppen and subnormalteiler endlicher grouppen. Math Z, 1962, 78: 202―221 doi: 10.1007/BF01195169
	Kurzweil H, Stellmacher B. The Theory of Finite Groups:An Introduction. New York: Springer-Verlag, 2004
	Ore O. Contributionsto the theory of groups. Duke Math J, 1939, 5: 431―460 doi: 10.1215/S0012-7094-39-00537-5
	Vasiliev A V, Vdovin E P. An adjacency criterionfor the prime graph of a finite simple group. Algebra and Logic, 2005, 6: 381―406 doi: 10.1007/s10469-005-0037-5
	Xu M Y. An Introduction to Finite Groups I. Beijing: Science Press, 1999 (in Chinese)

[1]	Xiaofeng CHEN, Jianlong CHEN. The (b; c)-inverse in semigroups and rings with involution[J]. Front. Math. China, 2020, 15(6): 1089-1104.
[2]	Yonghong HUANG, Shanzhong SUN. Non-embedding theorems of nilpotent Lie groups and sub-Riemannian manifolds[J]. Front. Math. China, 2020, 15(1): 91-114.
[3]	Hongzhi HUANG. Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry[J]. Front. Math. China, 2020, 15(1): 69-89.
[4]	Xingya FAN, Jianxun HE, Jinsen XIAO, Wenjun YUAN. Radon transforms on Siegel-type nilpotent Lie groups[J]. Front. Math. China, 2019, 14(5): 855-866.
[5]	Ruishu WANG, Xiaoshen WANG, Kai ZHANG, Qian ZHOU. Hybridized weak Galerkin finite element method for linear elasticity problem in mixed form[J]. Front. Math. China, 2018, 13(5): 1121-1140.
[6]	Huaquan WEI, Qiao DAI, Hualian ZHANG, Yubo LV, Liying YANG. On c^#-normal subgroups in finite groups[J]. Front. Math. China, 2018, 13(5): 1169-1178.
[7]	Tai Keun KWAK, Yang LEE, Young Joo SEO. Some remarks on one-sided regularity[J]. Front. Math. China, 2018, 13(4): 833-847.
[8]	Jia ZHANG, Baijun GAO, Long MIAO. Solvability of finite groups[J]. Front. Math. China, 2017, 12(6): 1501-1514.
[9]	Changqing XU, Yiran XU. Tensor convolutions and Hankel tensors[J]. Front. Math. China, 2017, 12(6): 1357-1373.
[10]	Sufang ZHANG,Kaitai LI,Hongen JIA. Two-grid stabilized mixed finite element method for fully discrete reaction-diffusion equations[J]. Front. Math. China, 2017, 12(2): 481-492.
[11]	Moritz GRUBER. Isoperimetry of nilpotent groups[J]. Front. Math. China, 2016, 11(5): 1239-1258.
[12]	Toma ALBU,Mihai IOSIF. New results on C₁₁ and C₁₂ lattices with applications to Grothendieck categories and torsion theories[J]. Front. Math. China, 2016, 11(4): 815-828.
[13]	Hongfei FU,Hongxing RUI,Zhaojie ZHOU. A posteriori error estimates for optimal control problems constrained by convection-diffusion equations[J]. Front. Math. China, 2016, 11(1): 55-75.
[14]	Yuemei MAO,Abid MAHBOOB,Wenbin GUO. S-semiembedded subgroups of finite groups[J]. Front. Math. China, 2015, 10(6): 1401-1413.
[15]	Mingzhong WU. Completable nilpotent Lie superalgebras[J]. Front. Math. China, 2015, 10(3): 697-713.

Viewed

Full text

Abstract

Cited

Shared

Discussed