in this paper we give a 2-generator 2-relation presentation for the group sl(2,121). this proves that sl(2,121), the covering group of psl(2,121), is efficient

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

In this paper we give a 2-generator 2-relation presentation for the group SL(2,121). This proves that SL(2,121), the covering group of PSL(2,121), is efficient

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

Every Seifert Fibre Group is the lift of a Fuchsian group to the universal covering group of PSL (2,R). From this, we work out a form of presentation for such a group. With the calculation of the Euler number, we can establish the presentation of the derived group of a Seifert Fibre Group

Using combinatorial methods, we prove the following theorem on the group S of all permutations of a countably-infmite set: Whenever p 6 S has infinite support without being a fixed-point-free involution, then any s G S is a product of three conjugates of p. Furthermore, we present uncountably many new conjugacy classes C of S satisfying that any s G S is a product of two elements of C. Similar ...

Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n) ©s R. Applying Bargmann’s theorem, we give explicit expressions for the liftings of project...