$Q$-perfect groups and universal $Q$-central extensions

Universal Locally Finite Central Extensions of Groups

DEFINITION. A group G is called a universal locally finite central extension of A provided that the following conditions are satisfied. (i) A <= (G (the centre of G). (ii) G is locally finite. (iii) (/1-injectivity). Suppose that A <= B <= D with A a (D, that D/A is finite, and that q>: B -> G is an ^-isomorphism (that is, q>{a) = a for all as A). Then there exists an extension q>: D -*• G of (...

Ramification Groups and Artin Conductors of Radical Extensions of Q

We study the ramification properties of the extensions Q(ζm, m √ a)/Q under the hypothesis that m is odd and if p | m than either p ∤ vp(a) or pvp(m) | vp(a) (vp(a) and vp(m) are the exponents with which p divides a and m). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we...

Central extensions of classical and quantum q-Virasoro algebras

We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra Aq,p(sl(N))c. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the...

Character Degrees of Extensions of PSL2(q) and SL2(q)

Denote by S the projective special linear group PSL2(q) over the field of q elements. We determine, for all values of q > 3, the degrees of the irreducible complex characters of every group H such that S 6 H 6 Aut(S). We also determine the character degrees of certain extensions of the special linear group SL2(q). Explicit knowledge of the character tables of SL2(q), GL2(q), PSL2(q), and PGL2(q...

Nonequivalent q-ary Perfect Codes