We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang–Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ...ordering or equivalently it is poly-Z.
Let p denote an odd prime. We show by example that the inequalities obtained in 6 for the behaviour of the cohomological index of a join of free Z/p-actions are sharp. Namely, for all odd integers ...k,l at least one of which is greater than one, we give examples of finite free Z/p-CW complexes of cohomological indices k and l whose join has index k+l+1 and also examples where the join has index k+l−1.
On Schur Rings over Infinite Groups Bastian, Nicholas; Brewer, Jaden; Humphries, Stephen ...
Algebras and representation theory,
06/2020, Volume:
23, Issue:
3
Journal Article
Peer reviewed
Open access
Schur rings are a type of subring of the group ring that is determined by a partition of the group. Past literature has exclusively focused on the finite group case. This paper extends many classic ...results about Schur rings to infinite groups, including Leung-Man’s classification of Schur rings over finite cyclic groups which is extended to the infinite cyclic group, as well as all torsion-free locally cyclic groups. Schurs rings over free groups and free products are also considered.
Nonabelian 2-groups
containing a cyclic subgroup of index 2 are dihedral groups, generalized quaternion groups, quasidihedral groups and modular maximal-cyclic groups. Earlier the authors introduced ...the classes of piecewise quasiaffine transformations on an arbitrary nonabelian 2-group
with a cyclic subgroup of index 2. For the generalized group of quaternions of order 2
we have obtained a complete classification of orthomorphisms, complete transformations and their left analogues in the class of piecewise quasiaffine transformations under consideration. This paper presents a similar classification for the remaining three groups (the dihedral group, the quasidihedral group and the modular maximal-cyclic group).
We extend work of Berdinsky and Khoussainov ‘Cayley automatic representations of wreath products’, International Journal of Foundations of Computer Science 27(2) (2016), 147–159 to show that being ...Cayley automatic is closed under taking the restricted wreath product with a virtually infinite cyclic group. This adds to the list of known examples of Cayley automatic groups.
Let
Φ
:
F
→
F
be an automorphism of the finite-rank free group
F
. Suppose that
G
=
F
⋊
Φ
Z
is word-hyperbolic. Then
G
acts freely and cocompactly on a CAT(0) cube complex.
With the increasing need for secure transmission and storage of medical images, the development of robust encryption algorithms is of paramount importance. Securing sensitive digital medical imagery ...information during transmission has emerged as a critical priority in the e-Healthcare systems. Recent research has highlighted the significance of developing advanced medical image encryption algorithms to ensure secure transmission during telediagnosis and teleconsultations. In this study, we propose a novel medical image encryption algorithm which is based on a novel substitution-box generation algebraic method using a combination of a multiplicative cyclic group with an order of 256 and a permutation group with a large order. To evaluate the security performance of the proposed generated S-box, various standard security indicators are assessed and analyzed. The newly proposed medical image encryption algorithm utilizes the generated S-box, along with bit-plane slicing, circular shifting, and XOR operations, to achieve enhanced security and robustness for encrypting sensitive imagery data. In order to assess the effectiveness of the proposed encryption algorithm, a comprehensive benchmarking analyses, specifically designed for evaluating image encryption schemes, have been conducted. The results obtained from the comparison and other analyses serve to validate the optimal features and high cryptographic strength exhibited by the proposed method. Hence, the proposed algorithm demonstrates significant effectiveness and holds considerable promise in the realm of medical image encryption for secure e-Healthcare systems.
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