Orbifolds and finite group representations by Li Chiang, Shi-Shyr Roan

“…We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. …”
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On the group pseudo-algebra of finite groups by Lewis, Mark L., Yan, Quanfu

“…Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C(G)=\lbrace (d,m_G(d))\mid d\in \mathrm{Cod} (G)\rbrace $, where $m_G(d)$ is the number of irreducible characters of $G$ with codegree $d\in \mathrm{Cod}(G)$. …”
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Finite groups whose coprime graphs are AT-free by Huani Li, Xuanlong Ma

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Finite Groups Which Are the Union of Autocentralizers of Some Automorphisms by Esmat Alamshahi, Mohammad Reza R. Moghaddam, Mohammad Amin Rostamyari

“…In this work, we study finite groups G, which can be written as the union of autocentralizers of some automorphisms of G. …”
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A note on p-solvable and solvable finite groups by R. Khazal, N. P. Mukherjee

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The normalizer problem for finite groups having normal $ 2 $-complements by Jidong Guo, Liang Zhang, Jinke Hai

“…Assume that $ H $ is a finite group that has a normal $ 2 $-complement. Under some conditions, it is proven that the normalizer property holds for $ H $. …”
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On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups by Jiangtao Shi, Cui Zhang

“…Let G be a finite group and 𝒩𝒞(G) the set of the numbers of conjugates of noncyclic proper subgroups of G. …”
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The Tracial Class Property for Crossed Products by Finite Group Actions by Xinbing Yang, Xiaochun Fang

“…Let A be an infinite dimensional simple unital tracial 𝒞-algebra with the (SP)-property, and let α:G→Aut(A) be an action of a finite group G on A which has the tracial Rokhlin property. …”
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A note on influence of subgroup restrictions in finite group structure by R. Khazal, N. P. Mukherjee

“…The structure of a finite group under specific restrictions respectively on its maximal, minimal and prime power subgroups has been investigated in this paper.…”
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A Note on the Normal Index and the c-Section of Maximal Subgroups of a Finite Group by Na Tang, Xianhua Li

“…Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K≤M and G=MH, we called the order of H/K the normal index of M and M∩H/K a section of M in G. …”
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Finite Groups of Order p2qr in which the Number of Elements of Maximal Order Is p3q∗ by Qingliang Zhang, Liang Xu

“…Let G be a finite group. We know that the order of G and the number of elements of maximal order in G are closely related to the structure of G. …”
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Finite Groups with the Same Order and the Same Number of Elements of Maximal Order as the Projective Special Linear Group L2q by Qingliang Zhang

“…Assume that G is a finite group. It is widely known that G and the number of elements of maximal order in G have something to do with the structure of G. …”
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On forbidden subgraphs of main supergraphs of groups by Xiaoyan Xu, Xiaohua Xu, Jin Chen, Shixun Lin

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Group-Valued Multisets by Andrei Alexandru, Gabriel Ciobanu

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Congruences associated with families of nilpotent subgroups and a theorem of Hirsch by Aivazidis, Stefanos, Müller, Thomas

“…Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order.…”
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Commutator Length of Finitely Generated Linear Groups by Mahboubeh Alizadeh Sanati

“…Finally we show that if 𝐺 is a soluble-by-finite group of Prüffer rank 𝑟 then cl(𝐺)≤𝑟(𝑟+1)/2+12𝑟3+𝑜(𝑟2), where 𝑜(𝑟2) is a quadratic polynomial in 𝑟.…”
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Anti- CC-Groups and Anti-PC-Groups by Francesco Russo

“…Analogously, a group G has polycyclic-by-finite classes of conjugate subgroups if the quotient group G/coreG(NG(H)) is a polycyclic-by-finite group for each subgroup H of G. An anti-PC group G is a group in which each nonfinitely generated subgroup K has the quotient group G/coreG(NG(K)) which is a polycyclic-by-finite group. …”
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Picard Groups of Algebraic Groups and an Affineness Criterion by Rosengarten, Zev

“…We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary group of finite exponent when $k$ is imperfect of characteristic $p$.…”
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On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras by Amir Sahami, Seyedeh Fatemeh Shariati

“…As an application, we show that for a left cancellative semigroup S, ℓ1S∗∗ is pseudo-contractible if and only if S is a finite group. We also study this property for φ-Lau product Banach algebras and the module extension Banach algebras.…”
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Groups with the same orders of Sylow normalizers as the Mathieu groups by Behrooz Khosravi, Behnam Khosravi

“…Also we prove that if G is a finite group, then G≅M if and only if for every prime q, |NM(Q)|=|NG(Q′)|, where Q∈Sylq(M) and Q′∈Sylq(G).…”
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