On Primitive Extensions of Rank 3 of Symmetric Groups

COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS

In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

Primitive rank 3 groups with a prime subdegree

As a continuation of the study of rank 3 permutation groups G begun in [4] we consider in this paper primitive rank 3 groups of even order in which the stabilizer Ga of a point a has an orbit of prime length. We show in particular that if G has no regular normal subgroup then the minimal normal subgroup M of G is a simple group of rank 3 and the constituent of 214, on the orbit of prime length ...

Primitive Permutation Groups of Finite Morley Rank

We prove a version of the O'Nan-Scott Theorem for detinably primitive permutation groups of finite Morley rank. This yields questions about structures of finite Morley rank of the form (F, + , . , / / ) where (F, +,.) is an algebraically closed field and H is a central extension of a simple group with /Y=sGL(rt, F). We obtain partial results on such groups H, and show for example that if char(/...

On Extensions of Simple Modules over Symmetric and Algebraic Groups

Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups

The main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3,q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2,q) and G > PSL(3,q).