Related papers: Coprime commutators in PSL(2,q)

Let $G$ be the simple algebraic group $\mathrm{SL}_2$ defined over an algebraically closed field $k$ of characteristic $p > 0$. Using results of A. Parker, we develop a method which gives, for any $q \in \mathbb{N}$, a closed form…

Using the corepresentation of the quantum group $ SL_q(2)$ a general method for constructing noncommutative spaces covariant under its coaction is developed. The method allows us to treat the quantum plane and Podle\'s' quantum spheres in a…

Let SL(2,q) be the group of 2X2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2,q) is the union of at least q-1 distinct conjugacy…

Modular double of quantum group SL_q(2,R) with |q|=1 has a series of selfadjoint irreducible representations parameterized by s. Ponsot and Teschner considered a decomposition of the tensor product of two representations into irreducibles.…

Let $L$ be an alternating prime non-split link in $S^3$. We use the category of flypes between reduced alternating diagrams for $L$ to classify involutions on $L$. As consequences, we show that the quotient of an alternating periodic link…

Let $G$ be a finite $p$-group whose derived subgroup $G'$ can be generated by $2$ elements. If $G'$ is abelian, Guralnick proved that every element of $G'$ is a commutator. In this paper, we prove that the condition that $G'$ should be…

Let $q$ be a prime power and $n$ and $r$ be positive integers. It is well known that the linearized binomial $L_r(x)=x^{q^r}+ax\in\mathbb{F}_{q^n}[x]$ is a permutation polynomial if and only if $(-1)^{n/d}a^{{(q^n-1)}/{(q^{d}-1)}}\neq 1$…

We complete the description of automorphism groups of all nonsplit extensions of elementary abelian $2$-groups by $PSL_2(q)$, with $q$ odd, for an irreducible induced action. An application of this result to the theory of $\pi$-submaximal…

The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this…

In this article we give examples which show that the TQFT representations of the mapping class groups derived from quantum SU(N) for N>2 are generically decomposable. One general decomposition of the representations is induced by the…

Let $\Bbb F_q$ be the finite field with $q$ elements and let $p=\text{char}\,\Bbb F_q$. It was conjectured that for integers $e\ge 2$ and $1\le a\le pe-2$, the polynomial $X^{q-2}+X^{q^2-2}+\cdots+X^{q^a-2}$ is a permutation polynomial of…

Given two polynomials $P(\underline x)$, $Q(\underline x)$ in one or more variables and with integer coefficients, how does the property that they are coprime relate to their values $P(\underline n), Q(\underline n)$ at integer points…

For all finite fields of $q$ elements where $q\equiv1\pmod4$ we have constructed permutation polynomials which have order 2 as permutations, and have 3 terms, or 4 terms as polynomials. Explicit formulas for their coefficients are given in…

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular…

For $p$ a prime, $G$ a finite group and $A$ a normal subset of elements of order $p$, we prove that if $A^2 = \{ab \mid a, b \in A\}$ consists of $p$-elements then $Q = \langle A \rangle$ is soluble. Further, if $O_p(G) = 1$, we show that…

We show that in characteristic 2, the Steinberg representation of the symplectic group Sp(2n,q), q a power of an odd prime p, has two irreducible constituents lying just above the socle that are isomorphic to the two Weil modules of degree…

In this paper, we prove that if G is a finite simple group with the same-size conjugacy class set U(G) = U(PSL(2, 11)), then G is isomorphic to PSL(2, 11).

In this paper, we prove that every PP is an AGW-PP. We also extend the result of Wan and Lidl to other permutation polynomials over finite fields and determine their group structure. Moreover, we provide a new general method to find the…

Let M be a compact closed non-orientable surface. We show that the space of representations of the fundamental group of M into PSL(2,R) has exactly two connected components. These two components are the preimages of a certain…

In this paper we discuss the permutational property of polynomials of the form $f(L(x))+k(L(x))\cdot M(x)\in \mathbb F_{q^n}[x]$ over the finite field $\mathbb F_{q^n}$, where $L, M\in \mathbb F_q[x]$ are $q$-linearized polynomials. The…