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A survey on enhanced power graphs of finite groups
Electronic Journal of Graph Theory and Applications, 2022 We survey known results on enhanced power graphs of finite groups. Open problems, questions and suggestions for future work are also included.
Xuanlong Ma +3 more
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Classification of finite groups that admit an oriented regular representation [PDF]
Bulletin of the London Mathematical Society, 2017 This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete answer to a 1980 ...
Joy Morris, Pablo Spiga
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On connectedness of power graphs of finite groups [PDF]
Journal of Algebra and its Applications, 2017 The power graph of a group [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices are adjacent if one is a power of the other.
Ramesh Prasad Panda, K. V. Krishna
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Journal of Pure and Applied Algebra, 2015 7 pages.
Caranti A, SCOPPOLA, CARLO MARIA
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Spectrum of commuting graphs of some classes of finite groups [PDF]
, 2016 In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups.
J. Dutta, R. K. Nath
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Which finite simple groups are unit groups? [PDF]
, 2014 We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear group $PSL_n ...
Davis, Christopher, Occhipinti, Tommy
core +2 more sources
The Quarterly Journal of Mathematics, 1987 This paper deals with the problem of enumerating the number f(n) of isomorphism types of groups of order n. There are three results which give upper bounds for f(n). The first bound holds for arbitrary groups, the second one deals with solvable groups, while the third one applies to groups with abelian Sylow subgroups.
Mciver, A, Neumann, P
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Inverse and stability theorems for approximate representations of finite groups [PDF]
, 2015 The -norm gives a useful measure of quasirandomness for real- or complex-valued functions defined on finite (or, more generally, locally compact) groups.
W. Gowers, O. Hatami
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Finite groups of units of finite characteristic rings [PDF]
, 2017 In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases.
Del Corso, I., Dvornicich, R.
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Neutrino mixing from finite modular groups [PDF]
Physical Review D, 2018 We study the lepton flavor models, whose flavor symmetries are finite subgroups of the modular group such as $S_3$ and $A_4$. In our models, couplings are also nontrivial representations of these groups and modular functions of the modulus.
Tatsuo C. Kobayashi +2 more
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