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- Title
On the commutativity probability in certain finite groups.
- Authors
Alajmi, Khaled
- Abstract
The purpose of this paper is to compute the probability Pr(G) that two elements of the group G, drawn at random with replacement, commute; that is, Pr(G) = Number of ordered pairs (x, y) ∈ G × G such that xy = yx/|G × G| = |G|² In particular, we compute Pr(G) for some groups such as the extraspecial groups of order p³, p prime, for the permutation groups G = Sn and G = An, n ≥ 5, for 10 non-abelian groups of order p4 and for simple groups of certain type.
- Subjects
FINITE groups; NONABELIAN groups; PROBABILITY theory; CONJUGACY classes; PERMUTATION groups; NILPOTENT groups; PERMUTATIONS
- Publication
International Journal of Mathematics & Computer Science, 2024, Vol 19, Issue 3, p613
- ISSN
1814-0424
- Publication type
Article