Results 1 to 10 of about 838,597 (95)
Rank three innately transitive permutation groups and related $2$-transitive groups [PDF]
Innov. Incidence Geom. 20 (2023) 135-175, 2022 The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This paper extends classifications of finite primitive and quasiprimitive groups of rank at most $3$ to a ...
arxiv +1 more source
Multiple transitivity except for a system of imprimitivity [PDF]
Journal of Group Theory, vol. 27, no. 4, 2024, pp. 651-712., 2022 Let $\Omega$ be a set equipped with an equivalence relation $\sim$; we refer to the equivalence classes as blocks of $\Omega$. A permutation group $G \le \mathrm{Sym}(\Omega)$ is $k$-by-block-transitive if $\sim$ is $G$-invariant, with at least $k$ blocks, and $G$ is transitive on the set of $k$-tuples of points such that no two entries lie in the same
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On the primitivity of Lai-Massey schemes [PDF]
Mediterranean Journal of Mathematics, 2021, 18(4), 165, 2020 In symmetric cryptography, the round functions used as building blocks for iterated block ciphers are often obtained as the composition of different layers providing confusion and diffusion. The study of the conditions on such layers which make the group generated by the round functions of a block cipher a primitive group has been addressed in the past
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On imprimitive rank 3 permutation groups [PDF]
J. London Math. Soc. (2011) 84 (3): 649-669, Erratum: J. London
Math. Soc. (2012) doi: 10.1112/jlms/jdr074, 2010 A classification is given of rank 3 group actions which are quasiprimitive but not primitive. There are two infinite families and a finite number of individual imprimitive examples. When combined with earlier work of Bannai, Kantor, Liebler, Liebeck and Saxl, this yields a classification of all quasiprimitive rank 3 permutation groups.
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A New Metric on Symmetric Group and Applications to Block Permutation Codes [PDF]
arXiv, 2021 Permutation codes have received a great attention due to various applications. For different applications, one needs permutation codes under different metrics. The generalized Cayley metric was introduced by Chee and Vu [4] and this metric includes several other metrics as special cases.
arxiv
Block Form of Frobenius Groups [PDF]
arXiv, 2020 The aim of this paper is to apply character properties of Frobenius group to a local block form of an group algebra. We start by establishing a block form of Brauer permutation Lemma by using block participation of conjugate classes of a group $G$. Then we can define a pair of Frobenius corresponding blocks between a group $G$ and its normal subgroup ...
arxiv
The lattice of submonoids of the uniform block permutations containing the symmetric group [PDF]
Semigroup Forum (2025)We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive under union and intersection by relating the submonoids containing the symmetric group to downsets in a new partial order on integer partitions. Furthermore, we show that the
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Multiparticle SUSY quantum mechanics and the representations of permutation group [PDF]
J.Phys.A33:1581,2000, 2000 The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into block-diagonal form with elementary matrix components are constructed.
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Free metabelian groups are permutation stable [PDF]
arXiv, 2023 We prove that all finitely generated free metabelian groups are permutation stable. This partially answers to the question asked by Levit and Lubotzky whether all finitely generated metabelian groups are permutation stable. Our proof extends the range of application of Levit-Lubotzky's method, which is used to show permutation stability of ...
arxiv
On finite permutation groups of rank three [PDF]
arXiv, 2023 The classification of the finite primitive permutation groups of rank $3$ was completed in the 1980s and this landmark achievement has found a wide range of applications. In the general transitive setting, a classical result of Higman shows that every finite imprimitive rank $3$ permutation group $G$ has a unique non-trivial block system $\mathcal{B ...
arxiv