Strong subgroup commutativity degree and some recent problems on the commuting probabilities of elements and subgroups

DOI10.2989/16073606.2016.1247118zbMath1436.20130arXiv1102.0509OpenAlexW2994859925MaRDI QIDQ5236150

Publication date: 15 October 2019

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0509

zbMATH Keywords

inequalities probability centralizers measure dihedral groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Probabilistic methods in group theory (20P05)

Related Items

The probability of commuting subgroups in arbitrary lattices of subgroups, Factorization number and subgroup commutativity degree via spectral invariants, Unnamed Item, Subgroup commutativity degree of profinite groups, Unnamed Item, Relative cyclic subgroup commutativity degrees of finite groups

Uses Software

Cites Work

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A survey on the estimation of commutativity in finite groups.
On the commuting probability and supersolvability of finite groups.
Subgroup S-commutativity degrees of finite groups.
Finite groups with three relative commutativity degrees.
Relative \(n\)-th non-commuting graphs of finite groups
Subgroup normality degrees of finite groups. I.
Addendum to ``Subgroup commutativity degrees of finite groups.
On the WGSC property in some classes of groups.
Probabilistic properties of the relative tensor degree of finite groups.
Groups of prime power order. Vol. 2.
On a lower bound of commutativity degree.
On the wgsc and qsf tameness conditions for finitely presented groups
Probability of mutually commuting \(n\)-tuples in some classes of compact groups
Subgroup commutativity degrees of finite groups.
On the commutativity degree of compact groups
What is the probability that two elements of a finite group commute?
Isoclinism classes and commutativity degrees of finite groups
Subgroup lattices of groups
A remark on the commuting probability in finite groups.
A formal identity involving commuting triples of permutations
Some inequalities of subgroup commutativity degree of finite groups.
A generalization of the probability that the commutator of two group elements is equal to a given element.
Universal commutator relations, Bogomolov multipliers, and commuting probability
Near abelian profinite groups
On the subgroup permutability degree of the simple Suzuki groups.
A classifying space for commutativity in Lie groups
Character degree sums of finite groups.
Commuting elements and spaces of homomorphisms
On topological filtrations of groups
On the exterior degree of the wreath product of finite Abelian groups.
Probability that the commutator of two group elements is equal to a given element.
Algebraic groups and Lie groups with few factors.
Non-commuting graph of a group.
On the commuting probability in finite groups.
The number of conjugacy classes in a finite group
On some problems of a statistical group theory. V
On some problems of a statistical group theory. VII
CENTRAL EXTENSIONS AND COMMUTATIVITY DEGREE
THE SUBGROUP COMMUTATIVITY DEGREE OF FINITE -GROUPS
ON THE TOPOLOGY OF THE NONABELIAN TENSOR PRODUCT OF PROFINITE GROUPS
COMMUTING ELEMENTS WITH RESPECT TO THE OPERATOR Λ IN INFINITE GROUPS
Limit points in the range of the commuting probability function on finite groups
SUBGROUP PERMUTABILITY DEGREE OF PSL(2,pⁿ)
The subgroup permutability degree of projective special linear groups over fields of even characteristic
COMMUTATIVITY DEGREE OF A CLASS OF FINITE GROUPS AND CONSEQUENCES
How many tuples of group elements have a given property? With an appendix by Dmitrii V. Trushin
FACTORIZATION NUMBERS OF SOME FINITE GROUPS
BOUNDS FOR THE RELATIVE n-TH NILPOTENCY DEGREE IN COMPACT GROUPS
COMMUTING POWERS AND EXTERIOR DEGREE OF FINITE GROUPS
A Generalization of Commutativity Degree of Finite Groups
SUBGROUP NORMALITY DEGREES OF FINITE GROUPS II
Remarks on the relative tensor degree of finite groups
Two Generalizations of the 5/8 Bound on Commutativity in Nonabelian Finite Groups
Commuting elements, simplicial spaces and filtrations of classifying spaces
CHARACTERS AND SOLUTIONS TO EQUATIONS IN FINITE GROUPS
The probability that a pair of elements of a finite group are conjugate
Higher commutativity and nilpotency in finite groups
Commutator maps, measure preservation, and 𝑇-systems
Commuting conjugacy classes: an application of Hall's marriage theorem to group theory
On Solutions of a Class of Equations in a Finite Group
The Number of Pairwise Non-Commuting Elements and the Index of the Centre in a Finite Group
What is the Probability an Automorphism Fixes a Group Element?
Several Conjectures on Commutativity in Algebraic Structures
What is the Probability that Two Group Elements Commute?
Normality degrees of finite groups
Hultman Numbers and Generalized Commuting Probability in Finite Groups
n-th Relative nilpotency degree and relative n-isoclinism classes
The probability that x and y commute in a compact group
Commuting elements in central products of special unitary groups
On the structure of spaces of commuting elements in compact Lie groups
SOME CONSEQUENCES OF THE EQUATION [xⁿ, y = 1 ON THE STRUCTURE OF A COMPACT GROUP]
THE PROBABILITY THAT AND COMMUTE IN A COMPACT GROUP
Addendum to: Permutability degrees of finite groups
Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups
Degree of commutativity of infinite groups
On the tensor degree of finite groups
COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS
On types and classes of commuting matrices over finite fields
A NEW CLASS OF ALMOST MEASURE PRESERVING MAPS ON FINITE SIMPLE GROUPS
On the average character degree of finite groups
A probabilistic meaning of certain quasinormal subgroups
On the Relative Commutativity Degree of a Subgroup of a Finite Group
Some Supersolvability Conditions for Finite Groups
On some problems of a statistical group-theory. I
On some problems of a statistical group-theory. II
On some problems of a statistical group-theory. III
On some problems of a statistical group-theory. IV