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Some properties of pair of n-isoclinism induction | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 15-26 اصل مقاله (315.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2022.20858.1330 | ||
| نویسندگان | ||
| M. Sajedi1؛ H. Darabi* 2 | ||
| 1Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran | ||
| 2Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran | ||
| چکیده | ||
| Let $(G,M)$ be a pair of groups, in which $M$ is a normal subgroup of a group $G.$ We study some properties of $n$-isoclinism of pair of groups. In fact, we show that the subgroups and quotient groups of two $n$-isoclinism pair of groups are $m$-isoclinic for all $m\le n.$ Moreover, the properties of $\pi$-pair and supersolvable pair of groups which are invariant under $n$-isoclinism has be studied. | ||
| کلیدواژه‌ها | ||
| Pair of groups؛ $n-$isoclinism؛ Supersolvable pair؛ $\pi-$seperable | ||
| مراجع | ||
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1. Sarah Butzman, G. Alan Cannon, Maria A. Paz, Centers of centralizer nearrings determined by all endomorphisms of symmetric groups, J. Algebra Relat. Topics, (2) 10 (2022) 13{26. 2. P. Hall, The classi cation of prime-power groups, J. Reine Angew. Math. 182 (1940) 130-141. 3. S. Heidarian and A.Gholami, On n-isoclinic pairs of groups, Algebra Colloq. 18 (2011) 999-1006. 4. M. Hashemi, M. Pirzadeh, S.A. Gorjian, The probability that the commutator equation [x,y]=g has solution in a nite group, J. Algebra Relat. Topics, (2) 7 (2019) 47-61. 5. M. Hassanzade, A. Pourmirzaei and S. Keyvanfar, On the nilpotency of a pair of groups, Southeast Asian Bull. Math. 37 (2013) 67-77. 6. N.S. Hekster, On the structure of n-isoclinism classes of groups, J. Pure Appl .Algebra, 40 (1986), 63-85. 7. M. R. R. Moghaddam, A. R. Salemkar and K. Chiti, n-Isoclinism classes and n-nilpotency degree of nite groups, Algebra Colloquim, 12 (2005), 255-261. 8. D.J.S. Robinson, A Course in the Theory of Groups, Springer Verlag, New York,1982. 9. A.R. Salemkar, F. Saeedi, T. Karimi, The structure of isoclinism classes of pair of groups, Southeast Asian Bull. Math. 31 (2007) 1173-1182. | ||
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آمار تعداد مشاهده مقاله: 203 تعداد دریافت فایل اصل مقاله: 249 |
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