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Equations in virtually class 2 nilpotent groups [PDF]
Groups, Complexity, Cryptology, 2022 We give an algorithm that decides whether a single equation in a group that is virtually a class $2$ nilpotent group with a virtually cyclic commutator subgroup, such as the Heisenberg group, admits a solution.
Alex Levine
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Secure Groups for Threshold Cryptography and Number-Theoretic Multiparty Computation
Cryptography, 2023 In this paper, we introduce secure groups as a cryptographic scheme representing finite groups together with a range of operations, including the group operation, inversion, random sampling, and encoding/decoding maps.
Berry Schoenmakers, Toon Segers
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A Class of Frobenius Groups [PDF]
Canadian Journal of Mathematics, 1959 If a group contains two subgroups A and B such that every element of the group is either in A or can be represented uniquely in the form aba', a, a’ in A, b ≠ 1 in B, we shall call the group an independent ABA-group. In this paper we shall investigate the structure of independent ABA -groups of finite order.A simple example of such a group is the group
Gorenstein, Daniel, Herstein, I. N.
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Conjugacy Class Sizes in Affine Semi-linear Groups [PDF]
Advances in Group Theory and Applications, 2020 The aim of this work is to study the structure and sizes of conjugacy classes in certain affine semi-linear groups. This provides a wealth of finite groups of small conjugate rank that are solvable and non-nilpotent.
Hossein Shahrtash
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ON A CLASS OF SUPERSOLUBLE GROUPS [PDF]
Bulletin of the Australian Mathematical Society, 2014 AbstractA subgroup $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H$ of a finite group $G$ is said to be S-semipermutable in $G$ if $H$ permutes with every Sylow $q$-subgroup of $G$ for ...
Ballester-Bolinches, Adolfo +3 more
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Class teachers and inclusion of marginalized groups of pupils in the class [PDF]
Revija za Elementarno Izobraževanje, 2018 In the first part of the article, we present the characteristics of marginalized groups of pupils and the role of the class teacher in integrating them into the class.
Anja Smole, Tina Vršnik Perše
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One-prime power hypothesis for conjugacy class sizes [PDF]
International Journal of Group Theory, 2017 A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition
Alan Camina, Rachel Camina
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Communications in Advanced Mathematical Sciences, 2019 The theory of $p$-ramification, regarding the Galois group of the maximal pro-$p$-extension of a number field $K$, unramified outside $p$ and $\infty$, is well known including numerical experiments with PARI/GP programs.
Georges Gras
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On finite groups with square-free conjugacy class sizes [PDF]
International Journal of Group Theory, 2018 We report on finite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.
Maria-Jose Felipe +2 more
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On the Class Group and the Local Class Group of a Pullback
Journal of Algebra, 1996 Let \(M\) be a non-zero maximal ideal of an integral domain \(T\), \(k=T/M\), \(\varphi: T\to k\) the natural homomorphism, and \(D\) a proper subring of \(k\). Let \(R\) be the pullback \[ \begin{tikzcd} R \ar[r] \ar[d] & D\ar[d] \\ T\ar[r,"\varphi"'] & k=T/M \quad .
FONTANA, Marco, Gabelli S.
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