The Dade group D(P ) of a finite p-group P , formed by equivalence classes of endopermutation modules, is a finitely generated abelian group. Its torsion-free rank equals the number of conjugacy classes of non-cyclic subgroups of P and it is conjectured that every nontrivial element of its torsion subgroup D(P ) has order 2, (or also 4, in case p = 2). The group D(P ) is closely related to the ...

Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups with automorphism group a p-group. Yet the goal of this paper is to prove that almost all finite p-groups do have automorphism group a p-group when p is odd. The asymptotic sense in which the theorem holds involves bounding the Frattini length of the p-gro...

Brualdi et al. introduced the concept of poset codes. In this paper, we consider the problem of classifying all perfect linear codes when the set of coordinate positions is endowed with crown poset structure. We derive a Ramanujan–Nagell type diophantine equation which is satis ed by parameters of perfect linear P-code. Solving this equation, we characterize parameters of one and two error corr...

Carbonyl-carbonyl (C=O···C'=O') interactions are ubiquitous in both small and large molecular systems. This interaction involves delocalization of a lone pair (n) of a donor oxygen into the antibonding orbital (π*) of an acceptor carbonyl group. Analyses of high-resolution protein structures suggest that these carbonyl-carbonyl interactions prefer to occur in pairs, that is, one donor per accep...

The reactions between fifteen carbonyl oxides and water have been investigated with the aim of contributing to a better understanding of the effects of the substituents in the reactivity of carbonyl oxides. We have employed density functional theory and large scale ab initio methods (CCSD(T), CASSCF, and CASPT2), combined with transition state theory, to investigate the addition of water to car...

We review the group structure of a cubic in the projective complex plane and give group theoretic formulations of some geometric properties of a cubic. Then, we apply them to pivotal isocubics, in particular to the cubics of Thomson, Darboux and Lucas. We use the group structure to identify different transformations of cubics. We also characterize equivalence of cubics in terms of the Salmon cr...

The notion of p-compact group [10] is a homotopy theoretic version of the geometric or analytic notion of compact Lie group, although the homotopy theory differs from the geometry is that there are parallel theories of p-compact groups, one for each prime number p. A key feature of the theory of compact Lie groups is the relationship between centers and fundamental groups; these play off agains...

let $g$ be a group and $h$ a subgroup of $g$‎. ‎ $h$ is said to have semi-$pi$-property in $g$ if there is a subgroup $t$ of $g$ such that $g=ht$ and $hcap t$ has $pi$-property in $t$‎. ‎in this paper‎, ‎investigating on semi-$pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.