Related papers: Totally orthogonal finite simple groups

Let $\mathrm{G} = \mathrm{Gl}_{n}(K)$, and $\mathrm{H} = \mathrm{G}^{\sigma}$ for $\sigma$ an involution of the form $g\rightarrow aga^{-1}$, It is known that for $K =\mathbb{Q}_q$ any irreducible representation of $\mathrm{G}$ with an…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

Let G be a connected unipotent group over a finite field F_q with q elements. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(F_q) and give an explicit description of…

In this paper, we consider the construction of irreducible representations of finite pattern groups in terms of Panov's associative polarization, which is a finite-field analogue of Kirillov's orbital method. Using this construction, first,…

We consider elements of finite order in the Riordan group $\cal R$ over a field of characteristic $0$. Viewing $\cal R$ as a semi-direct product of groups of formal power series, we solve, for all $n \geq 2$, two foundational questions…

Let G be a linear algebraic group defined over a finite field F_q. We present several connections between the isogenies of G and the finite groups of rational points G(F_q^n). We show that an isogeny from G' to G over F_q gives rise to a…

We investigate the finite-dimensional representation theory of two-parameter quantum orthogonal and symplectic groups that we found in [BGH] under the assumption that $rs^{-1}$ is not a root of unity and extend some results [BW1, BW2]…

We prove that there exists an integer-valued function f on positive integers such that if a finite group G has at most k real-valued irreducible characters, then |G/Sol(G)| is at most f(k), where Sol(G) denotes the largest solvable normal…

An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. This paper is about reversibles in the group $G$ of formally-invertible pairs of formal power series in two variables, with complex…

We construct explicit local systems on the affine line in characteristic $p>2$, whose geometric monodromy groups are the finite symplectic groups $Sp_{2n}(q)$ for all $n \ge 2$, and others whose geometric monodromy groups are the special…

The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…

Let G be a connected reductive group over a field of characteristic zero, and consider an orthogonal representation of G. We give a simple criterion for whether the representation lifts to the spin group, in terms of the highest weights of…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

Let $G$ be a connected reductive group defined over $\mathbb F_q$. Fix an integer $M\geq 2$, and consider the power map $x\mapsto x^M$ on $G$. We denote the image of $G(\mathbb F_q)$ under this map by $G(\mathbb F_q)^M$ and estimate what…

Carlitz proved that, for any prime power q other than 2, the group of all permutations of the finite field F_q is generated by the permutations induced by degree-one polynomials and x^{q-2}. His proof relies on a remarkable polynomial which…

We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order $q$, and $t$ fixes pointwise an $n$-space.…

We study the finite solvable groups $G$ in which every real element has prime power order. We divide our examination into two parts: the case $\textbf{O}_2(G)>1$ and the case $\textbf{O}_2(G)=1$. Specifically we proved that if…

For every integer $k$ there exists a bound $B=B(k)$ such that if the characteristic polynomial of $g\in \operatorname{SL}_n(q)$ is the product of $\le k$ pairwise distinct monic irreducible polynomials over $\mathbb{F}_q$, then every…

We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…