Abstract
The exterior degree of a pair of finite groups (G, N), which is a generalization of the exterior degree of finite groups, is the probability for two elements (g, n) in (G, N) such that g ⋀ n = 1. In the present paper, we state some relations between this concept and the relative commutatively degree, capability and the Schur multiplier of a pair of groups.
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References
Brown R., Loday J. -L.: Van Kampen theorems for diagrams of spaces. Topology 26, 311–335 (1987)
Brown R., Johnson D.L., Robertson E. F.: Some computations of nonabelian tensor products of groups. J. Algebra 111, 177–202 (1987)
Das A.K., Nath R.K.: On generalized relative commutativity degree of a finite group. Int. Electron. J. Algebra 7, 140–151 (2010)
Ellis G.: Capability, homology and a central series of a pair of groups. J. Algebra 179, 31–46 (1995)
Ellis G.: The Schur multiplier of a pair of groups. Appl. Categ. Structures 6(3), 355–371 (1998)
Ellis G.: On the relation between upper central quotients and lower central series of a group. Trans. Amer. Math. Soc. 353, 4219–4234 (2001)
G. Ellis, HAP–Homological Algebra Programming (2010), A refreed GAP 4 package (GAP Group 2008), available at http://hamilton.nuigalway.ie/Hap/www.
The GAP Group, GAP–Groups, Algorithms and Programming, Version 4.4. (2008), Available at: http://www.gap-system.org.
Erfanian A., Rezaei R., Lescot P.: On the relative commutativity degree of a subgroup of a finite group. Comm. Algebra 35, 4183–4197 (2007)
G. Karpilovsky, The Schur multiplier, London Math. Soc. Monogr. (N.S.) 2(1987).
Lescot P.: Isoclinism classes and commutativity degrees of finite groups. J. Algebra 177, 847–869 (1995)
Loday J.-L.: Cohomologie et groupe de Steinberg relatif. J. Algebra 54, 178–202 (1978)
Niroomand P., Rezaei R.: On the exterior degree of finite groups. Comm. Algebra 39(1), 335–343 (2011)
Rusin D.J.: What is the probability that two elements of a finite group commute?, Pacific J. Math. 82(1), 237–247 (1979)
Salemkar A., Tavallaee H., Mohammadzadeh H.: A remark on the commuting probability in finite groups. Southeast Asian Bull. Math. 34, 755–763 (2010)
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Niroomand, P., Rezaei, R. The Exterior Degree of a Pair of Finite Groups. Mediterr. J. Math. 10, 1195–1206 (2013). https://doi.org/10.1007/s00009-013-0252-6
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DOI: https://doi.org/10.1007/s00009-013-0252-6