Boundedly finite conjugacy classes of tensors

Bastos, Raimundo; Monetta, Carmine

doi:10.22108/ijgt.2020.124368.1643

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	Boundedly finite conjugacy classes of tensors
International Journal of Group Theory
دوره 10، شماره 4، اسفند 2021، صفحه 187-195 اصل مقاله (212.27 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2020.124368.1643
نویسندگان
Raimundo Bastos¹؛ Carmine Monetta^* ²
¹Departamento de Matemática, Universidade de Bras´ ılia, Brasilia-DF Brazil
²Dipartimento di Matematica, Università di Salerno, Salerno, Italy
چکیده
Let $n$ be a positive integer and let $G$ be a group‎. ‎We denote by $\nu(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$‎. ‎Set $T_{\otimes}(G) = \{g \otimes h \mid g,h \in G\}$‎. ‎We prove that if the size of the conjugacy class $\left \|x^{\nu(G)} \right\| \leq n$ for every $x \in T_{\otimes}(G)$‎, ‎then the second derived subgroup $\nu(G)''$ is finite with $n$-bounded order‎. ‎Moreover‎, ‎we obtain a sufficient condition for a group to be a BFC-group‎.
کلیدواژه‌ها
‎structure theorems‎, ‎finiteness conditions؛ non-abelian tensor square of groups

مراجع
[1] R. Bastos, I. N. Nakaoka and N. R. Rocco, Finiteness conditions for the non-abelian tensor product of groups, Monatsh. Math., 187 (2018) 603–615. [2] R. Bastos, I. N. Nakaoka and N. R. Rocco, The order of the non-abelian tensor product of groups, (2018), preprint available at ArXiV:1812.04747. [3] R. Brown, D. L. Johnson and E. F. Robertson, Some computations of non-abelian tensor products of groups, J. Algebra, 111 (1987) 177–202. [4] R. Brown and J.-L. Loday, Van Kampen theorems for diagrams of spaces, Topology, 26 (1987) 311–335. [5] E. Detomi, M. Morigi and P. Shumyatsky, BFC-theorems for higher commutator subgroups, Q. J. Math., 70 (2019). 849–858. [6] G. Dierings and P. Shumyatsky, Groups with boundedly finite conjugacy classes of commutators, Q. J. Math., 69 (2018) 1047–1051. [7] R. M. Guralnick and A. Maroti, Average dimension of fixed point spaces with applications, J. Algebra, 226 (2011) 298–308. [8] B. H. Neumann, Groups covered by permutable subsets, J. London Math. Soc., 29 (1954) 236–248. [9] M. Parvizi and P. Niroomand, On the structure of groups whose exterior or tensor square is a p-group, J. Algebra, 352 (2012) 347–353. [10] N. R. Rocco, On a construction related to the non-abelian tensor square of a group, Bol. Soc. Brasil Mat., 22 (1991) 63–79. [11] N. R. Rocco, A presentation for a crossed embedding of finite solvable groups, Comm. Algebra 22 (1994) 1975–1998. [12] J. Wiegold, Groups with boundedly finite classes of conjugate elements, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 238 (1957) 389–401.
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Boundedly finite conjugacy classes of tensors