The probability of nth degree for some nonabelian metabelian groups
A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the factor group, G/A is abelian. For any group G, the commutativity degree of G is the probability that two randomly selected elements in the group commute and denoted as P(G). Furthermore, the probability o...
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| Format: | Conference or Workshop Item |
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2013
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| Summary: | A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the factor group, G/A is abelian. For any group G, the commutativity degree of G is the probability that two randomly selected elements in the group commute and denoted as P(G). Furthermore, the probability of nth degree of a group G, Pn(G) is defined as the probability that the nth power of a random element commutes with another random element of the same group. It is also known as the nth commutativity degree of a group. In this paper, P(G) and Pn(G) for some nonabelian metabelian groups are determined. |
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