Related papers: Which alternating and symmetric groups are unit gr…

A Cayley digraph on a group $G$ is called NNN if the Cayley digraph is normal and its automorphism group contains a non-normal regular subgroup isomorphic to $G$. A group is called NNND-group or NNN-group if there is an NNN Cayley digraph…

We determine precisely when the branching coefficients arising from the restriction of irreducible representations of the symmetric group $S_n$ to the dihedral subgroup $D_n$ are nonzero, and we establish uniform linear lower bounds outside…

We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce that there exist C*-algebras that are not stably isomorphic to groupoid C*-algebras, though many of them are stably isomorphic to twisted groupoid C*-algebras.…

Let G be a noncyclic group of order 4, and let K be the ring Z of rational integers, the localization of Z at the prime 2 and the ring of 2-adic integers, respectively. We describe, up to conjugacy, all of the indecomposable subgroups in…

In this paper, we prove that if a finite group acts smoothly and effectively on an integral homology six-sphere and the fixed point set has an odd Euler characteristic, then the acting group is isomorphic to either the alternating group on…

Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that $p=\pm…

The spectrum of a finite group is the set of its elements orders. Groups are said to be isospectral if their spectra coincide. For every finite simple exceptional group $L=E_7(q)$, we prove that each finite group isospectral to $L$ is…

We give a review of recent works for non-associative algebras, especially Lie algebras satisfying the triality relation. They are also intimately related to S_4 (symmetric group of 4-objects) symmetry of the Lie algebras.

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…

We study some subgroups of the group of unitriangular automorphisms $U_n$ of a free associative algebra over a field of characteristic zero. We find the center of $U_n$ and describe the hypercenters of $U_2$ and $U_3$. In particular, we…

We classify isomorphism types of unital commutative algebras of rank 7 over an algebraically closed field of characteristic not 2 or 3 completely.

Let p be a prime, G a locally finite p-group, K a commutative ring of characteristic p. The anti-automorphism g\mapsto g\m1 of G extends linearly to an anti-automorphism a\mapsto a^* of KG. An element a of KG is called symmetric if a^*=a.…

Marks showed that $\mathbb{F}_2Q_8$, the $\mathbb{F}_2$ group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown…

I prove that the group of symmetries of the Tower of Hanoi graph with k pegs and n disks, denoted H_n^k, is isomorphic to the group of permutations of k elements, S_k, for all k greater than or equal to 3 and positive n.

We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representation theory to describe three cyclic and seven dihedral…

For a finite group $G$ denote by $N(G)$ the set of conjugesy class sizes of $G$. We show that every finite group $G$ with the property $N(G)=N(Alt_n), n>4$ or $N(G)=N(Sym_n), n>22$ is non-solvable.

Two $G$-sets ($G$ a finite group) are called linearly equivalent over a commutative ring $k$ if the permutation representations $k[X]$ and $k[Y]$ are isomorphic as modules over the group algebra $kG$. Pairs of linearly equivalent…

The main result of this paper shows that, over large enough fields of characteristic different from $2$, the alternating Hecke algebras are $\mathbb{Z}$-graded algebras that are isomorphic to fixed-point subalgebras of the quiver Hecke…

For simple twisted group algebra over a group $G$, if $G^{\shortmid}$ is Hall subgroup of $G$ then the semi-center is simple. Simple twisted groups algebras correspond to groups of central type. We classify all groups of central type of…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.