Related papers: Anticommutativity of Symmetric Elements under Gene…

Let $K$ be a field of characteristic two, and let $\lambda$ be a two-part partition of some natural number $r$. Denote the permutation module corresponding to the (maximal) Young subgroup $\Sigma_\lambda$ in $\Sigma_r$ by $M^\lambda$. We…

We continue the study of permutations of a finite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We…

Let $R$ be a commutative ring and ${\Bbb{A}}(R)$ be the set of ideals with non-zero annihilators. The annihilating-ideal graph of $R$ is defined as the graph ${\Bbb{AG}}(R)$ with the vertex set ${\Bbb{A}}(R)^*={\Bbb{A}}\setminus\{(0)\}$ and…

W.H.~Mills has determined, for a finitely generated abelian group $G$, the regular subgroups $N \cong G$ of $S(G)$, the group of permutations on the set $G$, which have the same holomorph of $G$, that is, such that $N_{S(G)}(N) =…

Let $G$ be a finite group. A coprime commutator in $G$ is any element that can be written as a commutator $[x,y]$ for suitable $x,y\in G$ such that $\pi(x)\cap\pi(y)=\emptyset$. Here $\pi(g)$ denotes the set of prime divisors of the order…

We develop a new criterion to tell if a group $G$ has the maximal gap of $1/2$ in stable commutator length (scl). For amalgamated free products $G = A \star_C B$ we show that every element $g$ in the commutator subgroup of $G$ which does…

The noncommutative (Cohn) localization S^{-1}R of a ring R is defined for any collection S of morphisms of f.g. projective left R-modules. We exhibit S^{-1}R as the endomorphism ring of R in an appropriate triangulated category. We use this…

We consider the group G of R-automorphisms of the polynomial ring R[x] especially in the case where R is the ring of integers modulo n. We describe conjugacy classes in G, and in the case where n = 4, we describe more explicitly the…

Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is…

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.…

Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…

We fix a field $\kk$ of characteristic $p$. For a finite group $G$ denote by $\delta(G)$ and $\sigma(G)$ respectively the minimal number $d$, such that for any finite dimensional representation $V$ of $G$ over $\kk$ and any $v\in…

For an orbifold X which is the quotient of a manifold Y by a finite group G we construct a noncommutative ring with an action of G such that the orbifold cohomology of X as defined in math.AG/0004129 by Chen and Ruan is the G invariant…

For finite groups $G$, we show that bosonic-fermionic coinvariant rings have a natural $U(\mathfrak{gl}(k|j)) \otimes \mathbb{C}[G]$-module structure. In particular, we show that their character series are a sum of super Schur functions…

With each antiholomorphic involution $\sigma $ of a connected complex semisimple Lie group $G$ we associate an automorphism $\epsilon_\sigma$ of the Dynkin diagram. The definition of $\epsilon_\sigma$ is given in terms of the Satake diagram…

Let $\Omega$ be a finite set and $T(\Omega)$ be the full transformation monoid on $\Omega$. The rank of a transformation $t\in T(\Omega)$ is the natural number $|\Omega t|$. Given $A\subseteq T(\Omega)$, denote by $\langle A\rangle$ the…

The property of $*$-cleanness in group rings has been studied for some groups considering the classical involution, given by $g^*=g^{-1}$. A group is called an SLC-group if its quotient by its center is isomorphic to the Klein group; these…

The third homology group of GL_n(R) is studied, where R is a `ring with many units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then H_3(GL_2(R), Q)…

We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible…

Recall that an element $x\in R$ is {\bf complemented} if there is a $y\in R$ such that $xy = 0$ and $x + y \in {\rm reg}(R)$. In a recent article [1], the authors investigated those rings for which every non-nilpotent element is…