Finite groups containing an intrinsic $2$-component of Chevalley type over a field of odd order

Finiteness Properties of Chevalley Groups over a Polynomial Ring over a Finite Field

It is known from work by H.Abels and P.Abramenko that for a classical Fqgroup G of rank n the arithmetic lattice G(Fq[t]) of Fq[t]-points is of type Fn−1 provided that q is large enough. We show that the statement is true without any assumption on q and for any isotropic, absolutely almost simple group G defined over Fq. Let k be a global function field and let G be a connected, noncommutative,...

Geometric Characterizations of Finite Chevalley Groups of Type B2

Finite Moufang generalized quadrangles were classified in 1974 as a corollary to the classification of finite groups with a split BN-pair of rank 2, by P. Fong and G. M. Seitz (1973), (1974). Later on, work of S. E. Payne and J. A. Thas culminated in an almost complete, elementary proof of that classification; see Finite Generalized Quadrangles, 1984. Using slightly more group theory, first W. ...

A Simple Classification of Finite Groups of Order p2q2

‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

Chevalley Groups over Commutative Rings

Wigner distributions for non Abelian finite groups of odd order

Wigner distributions for quantum mechanical systems whose configuration space is a finite group of odd order are defined so that they correctly reproduce the marginals and have desirable transformation properties under left and right translations. While for the Abelian case we recover known results, though from a different perspective, for the non Abelian case, our results appear to be new. ema...