for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. we give a short proof of a theorem of brandl, which classifies finite groups with $nu(g)=1$.

We describe the normal subgroup lattice of the automorphism groups of the countable universal homogeneous distributive lattice and of the countable atomless generalized Boolean lattice. Also, we show that subgroups of these automorphism groups of index less than 2@0 lie between the pointwise and the setwise stabilizer of a nite set.

Let G be a semi-simple Lie group and Γ < G be a lattice. This paper is motivated by the attempt to understand the infinite index subgroup structure of Γ . In particular, to understand the possibilities for infinite index, finitely generated, freely indecomposable, Zariski dense subgroups of Γ . The study of Zariski dense subgroups of semi-simple Lie groups has a long and rich history. Some high...

Let G be a rank 2 complete affine or hyperbolic Kac–Moody group over a finite field k. Then G is locally compact and totally disconnected. Let B− = HU− be the negative minimal parabolic subgroup of G, where H is the analog of a diagonal subgroup and U− is generated by all negative real root groups. Let w1 and w2 be the generators of the Weyl group. Let P − 1 = B − t Bw1B be the negative standar...

Let G be a group. We shall denote by L(G) the lattice formed by all subgroups of G. Two groups G and H are said to be lattice-isomorphic, or in short P-isomorphic, when their lattices L(G) and L(H) are isomorphic to each other. In this case the isomorphism from L(G) onto L(H) is called the L-isomorphism from G onto H. If G and H are isomorphic as groups, then G is clearly P-isomorphic to H. The...

Let [Formula: see text] be the simple group text], where is a prime number. For any subgroup of we compute Möbius function in lattice text]. To this aim, describe intersections maximal subgroups We point out some connections with other combinatorial objects, and, context, reduced Euler characteristic order complex subposet text]-subgroups for and power