Of special interest are those Lamé equations with finite monodromy group, having therefore algebraic solutions, studied by Baldassarri, Beukers and van der Waall, Chudnovsky and Chudnovsky, Dwork and many others (cf. [2], [4], [8] just to mention some papers). Lamé equations also occur in the context of Grothendieck’s p-curvature conjecture (cf. [8, p. 15]). This conjecture says that if the p-c...

Let G be a finite group. We shall designate the commutator subgroup of G by G2= [G, G]; this is the group generated by all commutators [g, h]=ghg~lh~1. Inductively G"=[Gn~~1, G] is defined to be the group generated by commutators of elements of G with elements of GB_1; and G* will designate HiT-i^"It should be recalled that G is nilpotent if G* =P, the subgroup consisting of the identity elemen...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

In this paper we study a key exchange protocol similar to DiffieHellman key exchange protocol using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no.92 of HallSenior table [15], for arbitrary prime p and show that for those groups, the group of central automorphisms commute. We use these for the key exchange we are studying. MSC: 94A62, 2...

‎for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎the aim of this paper is to classify all the non-nilpotent groups with $nu(g)=3$‎.

Introduction. A long-standing problem in group theory is to determine the number of non-isomorphic groups of a given order. The inverse problem–determining the orders for which there are a given number of groups–has received considerably less attention. In this note, we will give a characterization of those positive integers n for which there exist exactly 2 distinct groups of order n (up to is...

Let $G$ be a reductive group over an algebraically closed field $k$ of separably good characteristic $p>0$ for . Under these assumptions, Springer isomorphism $\phi : \mathcal {N}_{\mathrm {red}}(\mathfrak {g}) \rightarrow {V}_{\mathrm {red}}(G)$ from the nilpotent scheme $\mathfrak {g}$ to unipotent always exists and allows one integrate any $p$ -nilpotent element into One should wonder whe...

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...