[en] A complete description is given for the structure of a class of semigroups consisting of all abundant semigroups S in which the set of idempotents generates a regular subsemigroup such that S contains a multiplicative type A transversal. (author). 10 refs

[en] The least fundamental adequate good congruence on an arbitrary type W semigroup S is described as well as the largest superabundant full subsemigroup of S and the largest full subsemigroup of S which is a band of cancellative monoids. Weak type W semigroups are defined by replacing the idempotent-connected property in type W by one of its consequences and a structure theorem is obtained for such semigroups. (author). 12 refs

No abstract available

[en] Let G be a semi-simple linear algebraic group defined over an algebraically closed-field k. We describe the subgroups H of a parabolic P such that P/H is the affine line. (author). 4 refs

[en] The aim of this paper is to obtain a characterization of minimal prime ideals of (non-commutative) semigroups without nilpotent elements analogous to the one for the corresponding class of rings. We also define the notion of symmetric ideals of a semigroup and establish some of their basic properties. 5 refs

[en] Let PL(F_q) denote the projective line over a Galois field F_q. Consider PSL(2,Z) as a free product of two cyclic groups < x > and < y > of orders 2 and 3. We have shown that any homomorphism from PSL(2,Z) into PGL(2,q) can be extended to a homomorphism from PGL(2,Z) into PGL(2,q) except in the case where the order of the image of xy is 6 but the images of x and y do not commute in PGL(2,q). It has been shown also that every element in PGL(2,q), not of order 1,2 or 6, is the image of xy under some non-degenerate homomorphism. We have parametrized the conjugacy classes of non-degenerate homomorphisms α with the non-trivial elements of F_q. Due to this parametrization we have developed a useful mechanism by which one can construct a unique coset diagram (attributed to G. Higman) for each conjugacy class, depicting the action of PGL(2,Z) on PL(F_q). (author). 9 refs

[en] A method of characterizing a class of semigroups is described and a structure theorem for this class of semigroups is given. This class of semigroups consists of all abundant semigroups S in which the set of idempotents generates a regular subsemigroup and possesses a normal medial idempotent u such that uSu is a type A semigroup. (author). 9 refs

[en] PSL(2,q) is the projective special linear group. The automorphism group of PSL(2,q) is denoted by PΓL(2,q). The structure of PΓL(2,q) is well-known, it is isomorphic to the semidirect product of PGL(2,q) by a cyclic group A of order n, where q=pⁿ, p a prime. Taking α is an element of PΓL(2,q) such that α²=1 by considering conjugacy classes of involutions in PΓL(2,q) and finding the centralizer of this element in PSL(2,q) we prove the following result. Theorem: Let α be an involutary automorphism of PSL(2,q) where q is odd and q ≥ 5. Then (i) if q is not a square the fixed point set of α is either dihedral of order q-1 or dihedral of order q+1. (ii) If q=r² the fixed point set of α is either dihedral of order q-1, or dihedral of order q+1 or is isomorphic to PGL(2,r). (author). 2 refs

[en] We introduce pure radical of an ideal in a semigroup with zero. For this purpose we define pure, semipure and other related types of ideals, and establish some of their basic properties. 1 ref

[en] In a previous paper, the author discussed the existence and the structure of finite groups with four generators a,b,c and d when the orders of b,c,d are respectively p,p,q with p< q. The case p< q, or equivalently the case when the orders of b,c,d are respectively p,q,q with p< q is discussed in the present paper. As in the previous paper, the order m of a is arbitrary but m is not an element of the set containing p,q