Results 1 to 10 of about 816 (183)
On subpolygroup commutativity degree of finite polygroups [PDF]
AIMS Mathematics, 2023 <abstract><p>Probabilistic group theory is concerned with the probability of group elements or group subgroups satisfying certain conditions. On the other hand, a polygroup is a generalization of a group and a special case of a hypergroup. This paper generalizes probabilistic group theory to probabilistic polygroup theory.
M Al Tahan +2 more
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Commutativity Degree of Crossed Modules
TURKISH JOURNAL OF MATHEMATICS, 2021 Summary: In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in \textsf{GAP} and classify crossed modules by using this function.
Arvasi, Zekeriya +2 more
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The degree of commutativity and lamplighter groups [PDF]
International Journal of Algebra and Computation, 2018 The degree of commutativity of a group [Formula: see text] measures the probability of choosing two elements in [Formula: see text] which commute. There are many results studying this for finite groups. In [Y. Antolín, A. Martino and E. Ventura, Degree of commutativity of infinite groups, Proc. Amer. Math. Soc.
Cox, Charles Garnet
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On generalized commutativity degree of a finite group
Rocky Mountain Journal of Mathematics, 2011 Let \(G\) be a finite group. The generalized commutator of an \(n\)-tuple \((x_1,x_2,\dots,x_n)\in G^n\) is defined as the product \(x_1x_2\cdots x_nx_1^{-1}x_2^{-1}\cdots x_n^{-1}\). The object of this paper is to study the probability that the generalized commutator of an arbitrarily chosen \(n\)-tuple of group elements equals a given group element \(
Nath, R.K., Das, A.K.
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Subgroup commutativity degrees of finite groups
Journal of Algebra, 2009 Let \(G\) be a finite group and let \(L(G)\) be the set of subgroups of \(G\). The author defines the subgroup commutativity degree of \(G\) by \(\text{sd}(G)=|L(G)|^{-2}|\{(H,K)\in L(G)^2\mid HK=KH\}|\). Clearly, \(\text{sd}(G)\) is the probability that two subgroups of \(G\) permute. The author states some simple general properties of \(\text{sd}(G)\)
Marius Tarnauceanu
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Finite Groups with Five Relative Commutativity Degrees
Results in Mathematics, 2022 We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
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Subgroup S-commutativity degrees of finite groups
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2012 The so--called subgroup commutativity degree $sd(G)$ of a finite group $G$ is the number of permuting subgroups $(H,K) \in \mathrm{L}(G) \times \mathrm{L}(G)$, where $\mathrm{L}(G)$ is the subgroup lattice of $G$, divided by $|\mathrm{L}(G)|^2$. It allows us to measure how $G$ is far from the celebrated classification of quasihamiltonian groups of K ...
Francesco G Russo
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FINITENESS OF COMMUTABLE MAPS OF BOUNDED DEGREE [PDF]
Bulletin of the Korean Mathematical Society, 2015 In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Pre(f) has only finitely many endomorphisms (respectively polynomial maps) of bounded degree which are commutable with f.
Lee, Chong Gyu, Ye, Hexi
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Degree estimate for commutators
Journal of Algebra, 2009 18 ...
Drensky, V, Yu, JT
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Degree of commutativity of infinite groups [PDF]
Proceedings of the American Mathematical Society, 2016 11 ...
Antolin, Yago +2 more
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