‎Let $G$ be a finite $p$-group of order $p^n$ and‎ ‎$|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$‎, ‎where ${mathcal M}(G)$‎ ‎is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer‎. ‎The classification of such groups $G$ is already known for $t(G)leq‎ ‎6$‎. ‎This paper extends the classification to $t(G)=7$.

Nontrivial difference sets in groups of order a power of 2 are part of the family of difference sets called Menon difference sets (or Hadamard), and they have parameters (22d+2, 22d+1±2d, 22d±2d). In the abelian case, the group has a difference set if and only if the exponent of the group is less than or equal to 2d+2. In [14], the authors construct a difference set in a nonabelian group of ord...

Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localised particles carrying charges relat...

‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

This is an introduction to work on the generalisation to quantum groups of Mackey’s approach to quantisation on homogeneous spaces. We recall the bicrossproduct models of the author, which generalise the quantum double. We describe the general extension theory of Hopf algebras and the nonAbelian cohomology spaces H(H,A) which classify them. They form a new kind of topological quantum number in ...

Superimposed D–branes have matrix–valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativi...

In our paper referred to above we claim to enumerate all …nite primitive linear groups of prime degree r over C with a nonabelian socle. However, the case where the socle is imprimitive was overlooked. In the present paper we deal with this case to complete the classi…cation. 2000 Mathematics Subject Classi…cation: 20H20 20C15 20C33 In the paper referred to above, we state a theorem (Theorem 1....

Let G be a finite group. An irreducible character χ is called monolithic when the factor group G/ker⁡(χ) has unique minimal normal subgroup. In this paper, we prove that for smallest prime q dividing order of if faithful imprimitive degree q, then becomes nonabelian q-group or Frobenius with cyclic complement whose q. Under certain conditions, also classify groups in which their nonlinear chara...

Let $X$ be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, closed subset which is disk Cantor set removed from its interior. For example, could any surface of type only finitely boundary components. We prove that the mapping class group does not satisfy Tits Alternative. That is, Map$(X)$ contains generated subgroup virtually solvable and no nonabe...