On Huppert's conjecture for F_4(2) by Hung P Tong-Viet, Thomas P Wakefield

“…Let $G$ be a finite group and let $text{cd}(G)$ be the set of all complex irreducible character degrees of $G$. …”
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Witten index and wall crossing by Hori, K, Kim, H, Yi, P

“…In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. …”

Some problems in the theory of finite insoluble groups by Collins, M

“…<p>In this thesis, a study is made of finite groups which satisfy the following hypothesis:-<br/> <p>(*) G is a finite group admitting an automorphism α of order r with a fixed point subgroup of order q, where q and r are distinct prime numbers.…”

A question of Malinowska on sizes of finite nonabelian simple groups in relation to involution sizes by Anabanti, Chimere Stanley

“…Let $I_n(G)$ denote the number of elements of order $n$ in a finite group $G$. Malinowska recently asked “what is the smallest positive integer $k$ such that whenever there exist two nonabelian finite simple groups $S$ and $G$ with prime divisors $p_1,\,\cdots ,\,p_k$ of $|G|$ and $|S|$ satisfying $2=p_1<\,\cdots \, and $I_{p_i}(G)=I_{p_i}(S)$ for all $i \in \lbrace 1,\,\cdots ,\,k\rbrace $, we have that $|G|=|S|$?”. …”
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The fields of values of characters of degree not divisible by p by Gabriel Navarro, Pham Huu Tiep

“…We study the fields of values of the irreducible characters of a finite group of degree not divisible by a prime p. In the case where $p=2$, we fully characterise these fields. …”
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Neutrosophic General Machine: A Group-Based Study by Marzieh Shamsizadeh, Parvaneh Lo′lo

“…This study aims to develop the notion of neutrosophic single-valued general machine over a finite group, which is knows as ”group neutrosophic general machine”, for simplicity, GNGM. …”
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A new characterization of PSL(2, 25) by Syyed Sadegh Salehi Amiri, Alireza Khalili Asboei

“…Let G be a finite group and pi_{e}(G) be the set of element orders of G. …”
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Coset decision trees and the Fourier algebra by Sanders, T

“…We show that if G is a finite group and f is a {0, 1}-valued function on G with Fourier algebra norm at most M, then f may be computed by the coset decision tree (that is a decision tree in which at each vertex we query membership of a given coset) having at most (exp(exp(exp(O(M2))))) leaves. …”

The Schur multiplier, profinite completions and decidability by Bridson, M

“…We prove that there is no algorithm that, given a finitely presented, residually finite group $G$ and a finitely presentable subgroup $P\subset G$, can determine whether or not $\hat P\to\hat G$ is an isomorphism.…”

Profinite rigidity and surface bundles over the circle by Bridson, MR, Reid, AW, Wilton, H

“…Thus, regardless of betti number, if M and N are punctured torus bundles over the circle and M is not homeomorphic to N, then there is a finite group G such that π1M maps onto G and π1N does not.…”

A general case of the commutativity degree of nilpotent p-groups of class two by Sarmin, Nor Haniza

“…Given a finite group, the commutativity degree of the group is defined as the probability that two elements of the group, chosen randomly with replacement, commute. …”

Order Sum Graph of a Group by Javeria Amreen, Sudev Naduvath

“… The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. …”
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Branching rules in the ring of superclass functions of unipotent upper-triangular matrices by Nathaniel Thiem

“…It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the classical representation theory of the symmetric group. …”
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Equivariant index bound for min–max free boundary minimal surfaces by Franz, Giada

“…Abstract Given a three-dimensional Riemannian manifold with boundary and a finite group of orientation-preserving isometries of this manifold, we prove that the equivariant index of a free boundary minimal surface obtained via an equivariant min–max procedure á la Simon–Smith with n-parameters is bounded above by n.…”
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Profinite completions of free-by-free groups contain everything by Bridson, MR

“…Given an arbitrary, finitely presented, residually finite group Γ, one can construct a finitely generated, residually finite, free-by-free group <em>M</em>_Γ = <em>F</em>_∞ ⋊ <em>F</em>₄ and an embedding <em>M</em>_Γ ↪ (<em>F</em>₄ ∗ Γ) × <em>F</em>₄ that induces an isomorphism of profinite completions. …”

Separating invariants and local cohomology by Dufresne, E, Jeffries, J

“…The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. …”

Deficiency, relation gap and two-dimensional groups by Kar, A, Nikolov, NV

“…Let G be a finitely presented, residually finite group and let δ(G) denote the deficiency of G . …”

Relative commutativity degree of some dihedral groups by Abdul Hamid, M., Mohd. Ali, N. M., Sarmin, N. H., Abd. Manaf, F. N.

“…The commutativity degree of a finite group G was introduced by Erdos and Turan for symmetric groups, finite groups and finite rings in 1968. …”

Group Rings Satisfying Generalized Engel Conditions by Mojtaba Ramezan-Nassab

“…Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1)  y]=[[x ,_( n)  y]  , y]. …”
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Groups with Two Extreme Character Degrees and their Minimal Faithful Representations by Mahtab Delfani, Houshang Behravesh

“…for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. …”
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