Related papers: (p,q,r)-Generations for Janko Groups $J_1$ and $J_…
This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.
All quantum group structures on the group GL(2) are classified. It is shown that there are only two such structures, the well known quantum groups GL$_{qp}$(2) and GL$_{hh'}$(2).
No abstract available.
Using the Luthar--Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the…
We classify finite $p$-groups, upto isoclinism, which have only two conjugacy class sizes $1$ and $p^3$. It turns out that the nilpotency class of such groups is $2$.
Preliminary results of a selected few recent experiments at JLab are presented.
We determine the structure of biquasigroups (Q,^,*) satisfying varations of Polonijo's Ward double quasigroup identity (x^z)*(y^z)=x*y, including those that are linear over a group.
Some question about representations of $p$-adic groups are discussed.
The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2-subgroups are considered. It is proved that the direct square…
The present note shows that $\mathcal{Q}$-groups in [H. Heineken and F.G. Russo, Groups described by element numbers, Forum Math. 27 (2015), 1961--1977] are solvable groups (not necessarily nilpotent) for which the equation $T_G(r,s)=0$ is…
We give a uniform construction of the finite simple groups $E_6(q)$, $F_4(q)$ and ${}^2E_6(q)$, which does not require any special treatment for characteristics 2 or 3, and in particular avoids any mention of quadratic Jordan algebras.…
We determine the characters of SL(2) representations of groups and surface groups.
A J{\o}rgensen group is a non-elementary Kleinian group that can be generated by two elements for which equality holds in J{\o}rgensen's Inequality. This paper shows that the only torsion-free J{\o}rgensen group is the figure-eight knot…
We record for reference a detailed description of the automorphism groups of the groups of order $p^{2} q$, where $p$ and $q$ are distinct primes.
This paper has been withdrawn and no version of it will ever be published.
We extend the results of \cite{EJK} on property (T) to certain groups "coordinatized" by nonassociative algebras.
We review certain basic geometric and analytic results concerning MVW-extensions of classical groups, following Moeglin-Vigneras-Waldspurger. The related results for Jacobi groups, metaplectic groups, and special orthogonal groups are also…
In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6.
We prove the existence of abelian, solvable and nilpotent definable envelopes for groups definable in models of an NTP2 theory.
We calculate extensions between certain irreducible admissible representations of p-adic groups.