What is the Probability that Two Group Elements Commute?
From MaRDI portal
Publication:4403059
DOI10.2307/2318778zbMath0276.60013OpenAlexW4233041860MaRDI QIDQ4403059
Publication date: 1973
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2318778
Combinatorial probability (60C05) Abstract finite groups (20D99) Compact groups (22C05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05)
Related Items
Conjugacy classes of \(\pi \)-elements and nilpotent/abelian Hall \(\pi \)-subgroups, Two Quasigroup Elements Can Commute With Any Positive Rational Probability, Limit points of commuting probabilities of finite groups, Compact groups with probabilistically central monothetic subgroups, The average character degree of finite groups and Gluck's conjecture, The Order Product Prime Probability and Commutativity Degree for Some Finite Groups, The average conjugacy class size and the Hall π-subgroups in π-solvable groups, On the commuting probability of \(p\)-elements in a finite group, Nilpotent probability of compact groups, Finite groups with many \(p\)-regular conjugacy classes, Supersolvability and nilpotency in terms of the commuting probability and the average character degree, Characterization and commuting probability of n-centralizer finite rings, Unnamed Item, Some numerical results on the wreath product of \(Z_p\) and \(Z_{p^n}\), On generalized probability in finite commutative rings, ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS, On commuting probabilities in finite groups and rings, Conjugacy classes of \(p\)-elements and normal \(p\)-complements, BOUNDS FOR THE RELATIVE n-TH NILPOTENCY DEGREE IN COMPACT GROUPS, The probability that the commutator equation [x,y=g has solution in a finite group], On the commuting probability for subgroups of a finite group, A Generalization of Commutativity Degree of Finite Groups, Signed Hultman numbers and signed generalized commuting probability in finite groups, Degree of commutativity of infinite groups, Cyclicity degrees of finite groups., Probabilistically-like nilpotent groups, COMMUTATOR EQUATIONS IN FINITE GROUPS, A generalization of a question asked by B. H. Neumann, Subnormalizers and solvability in finite groups, Non-commuting graphs and some bounds for commutativity degree of finite Moufang loops, On groups with large character degree sums., THE PROBABILITY OF ZERO MULTIPLICATION IN FINITE RINGS, Finite Groups with Four Relative Commutativity Degrees, Unnamed Item, Commutativity Degree of Crossed Modules, Unnamed Item, Applying extremal graph theory to a question on finite groups, On the commuting probability and supersolvability of finite groups., The Commutativity Degree in the Class of Nonabelian Groups of Same Order, Gaps in probabilities of satisfying some commutator-like identities, \(q\)-tensor and exterior centers, related degrees and capability, Compact groups with high commuting probability of monothetic subgroups, How Hamiltonian can a finite group be?, Groups satisfying identities with high probability, Rational growth and degree of commutativity of graph products, On two- and three-element subsets of groups, Word problems for finite nilpotent groups, What is the probability an automorphism fixes a group element?, On the character degree sums, On the number of conjugacy classes of \(\pi\)-elements in finite groups., A note on subgroup commutativity degrees of finite groups, On the probability that an automorphism of a group fixes an element of the group, Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements, Characterization of rings with nullity degree at least 1 4, Largeness and equational probability in groups, On generalized commutativity degree of a finite group., On the nilpotent probability and supersolvability of finite groups, On the average character degree and the average class size in finite groups., On asymptotic commutativity degree of finite groups, Probabilistic aspects of ZM-groups, Commuting probabilities of infinite groups, Probability that the commutator of two group elements is equal to a given element., On some probabilistic aspects of (generalized) dicyclic groups, On the commutativity degree of a group algebra, THE PROBABILITY OF AN AUTOMORPHISM FIXING A SUBGROUP ELEMENT OF A FINITE GROUP, RELATIVE NON-COMMUTING GRAPH OF A FINITE GROUP, The probability that x and y commute in a compact group, A NOTE ON THE RELATIVE COMMUTATIVITY DEGREE OF FINITE GROUPS, Addendum to paper ``On the commuting probability in finite groups., Subgroup normality degrees of finite groups. I., Universal commutator relations, Bogomolov multipliers, and commuting probability, THE PROBABILITY THAT AND COMMUTE IN A COMPACT GROUP, On a lower bound of commutativity degree., On the Relative Commutativity Degree of a Subgroup of a Finite Group, On the commuting probability in finite groups., Algorithmic problems in Engel groups and cryptographic applications, n-Isoclinism Classes and n-Nilpotency Degree of Finite Groups, Non-commuting graphs of certain almost simple groups, ELEMENTS WITH SQUARE ROOTS IN COMPACT GROUPS, On the Probability That an Automorphism Fixes a Group Element, The range of thresholds for diameter 2 in random Cayley graphs, Some results on relative commutativity degree., Minimal order semigroups with specified commuting probability., On the Exterior Degree of Finite Groups, The Conjugacy Ratio of Groups, ON THE PROBABILITY OF GENERATING NILPOTENT SUBGROUPS IN A FINITE GROUP, The breadth-degree type of a finite \(p\)-group, Unnamed Item, A note on the commutativity of groups, Subgroup commutativity degrees of finite groups., A probabilistic measure for the number of commuting subgroups in locally compact groups, Subgroups with large relative commutativity degree, Strong subgroup commutativity degree and some recent problems on the commuting probabilities of elements and subgroups, Hultman Numbers and Generalized Commuting Probability in Finite Groups, Finite groups with five relative commutativity degrees, Subnormalizers and the degree of nilpotence in finite groups, On the \({p}\)-closedness and \({p}\)-nilpotency of finite groups, On the commutativity degree of compact groups, Unnamed Item, Limit points in the range of the commuting probability function on finite groups, On the Order of the Automorphism Group of a Finite Group, SCHUR’S COLOURING THEOREM FOR NONCOMMUTING PAIRS, SUBGROUP PERMUTABILITY DEGREE OF PSL(2,pn), Planar, Toroidal, and Projective Commuting and Noncommuting Graphs, Invariant metrics on finite groups, Unnamed Item, Probabilistically nilpotent groups, The probability that the multiplication of two ring elements is zero, Relative cyclic subgroup commutativity degrees of finite groups, Probability that an autocommutator element of a finite group equals to a fixed element, COMMUTING PROBABILITY OF COMPACT GROUPS, The number of conjugacy classes in a finite nilpotent group
