We derive presentations of the interval groups related to all quasi-Coxeter elements in Coxeter group type D n . Type is only infinite family finite that admits proper elements. The we obtain are over a set generators bijection with what call Carter generating set, and relations those defined by diagram together twisted cycle or commutator relator, depending on whether element not. proof based ...

The purpose of this note is to record for my algebra class a proof of the Inverse Galois Problem for finite abelian groups. Recall that the Inverse Galois Problem is stated as follows: Given a finite group G, is there a Galois extension Q ⊆ K such Gal(K/Q) = G? The crucial point in the problem is that the base field is Q, since given any finite group G, there is a Galois extension of fields F ⊆...

We describe trial and error computer programs for finding certain homomorphisms of a knot group on a special projective group LF(2, p), p prime, and programs to evaluate #i(3TC ; Z) where 9TC is a finitely sheeted branched covering space of S3 associated with such a homomorphism. These programs have been applied to several collections of examples, in particular to the Kinoshita-Terasaka knots, ...

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This paper is dedicated to Walter Feit on the occasion of his 65th birthday. Its contents were presented in part at the 1995 Ohio State finite group representation conference organized in celebration of that birthday. Primarily, the paper is a discussion of some classical and recent developments in the modular representation theory of finite groups of Lie type, and the problems which drive that...

If G is a finitely generated profinite group then the verbal subgroup Gq is open. In a d-generator finite group every product of qth powers is a product of f(d, q) qth powers. 20E20, 20F20.

Finite Groups 20Dxx [1] A. Adem, J. F. Carlson, D. B. Karagueuzian, and R. James Milgram, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, J. Pure Appl. Algebra 164 (2001), no. 3, 275–305. MR MR1857743 (2002g:20089) [2] Faryad Ali and Jamshid Moori, Fischer-Clifford matrices of the non-split group extension 2 · U4(2), Quaest. Math. 31 (2008), no. 1, 27–36. MR MR2404644 [3] Habib...

The study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given–three using symmetric function theory and one using Markov chains. This leads to non-trivial enumerative results. Cycle index...

About 60 years ago H. Zassenhaus 17] classiied nite near-elds. In doing so he also gave a full description of those nite groups which have a representation D (over C) such that D(g) has no eigenvalue 1 for any nontrivial element g 2 G. In our terminology such a group is called semiregular. One of the results in 17] characterizes SL 2 (5) as the only perfect semiregular group. Clearly, if the un...