Let $G$ be a finite group. The graph $D(G)$ is a divisibility graph of $G$. Its vertex set is the non-central conjugacy class sizes of $G$ and there is an edge between vertices $a$ and $b$ if and only if $a|b$ or $b|a$. In this paper, we investigate the structure of the divisibility graph $D(G)$ for a non-solvable group with $sigma^{ast}(G)=2$, a finite simple group $G$ that satisfies the one-p...

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 ...

Bloodstream trypanosomes evade the immune system of their mammalian host by sequentially expressing a large number of different variable surface glycoproteins (VSGs). In contrast, metacyclic trypanosomes, the final developmental stage in the tsetse fly, express a much more restricted set of VSGs. These metacyclic VSGs are the first to be exposed to the immune system of the mammalian host after ...

Attempts to recreate all the developmental stages of Trypanosoma cruzi in vitro have thus far been met with partial success. It is possible, for instance, to produce trypomastigotes in tissue culture and to obtain metacyclic trypomastigotes in axenic conditions. Even though T. cruzi amastigotes are known to differentiate from trypomastigotes and metacyclic trypomastigotes, it has only been poss...

Metacirculants are a basic and well-studied family of vertex-transitive graphs, and weak metacirculants are generalizations of them. A graph is called a weak metacirculant if it has a vertex-transitive metacyclic automorphism group. This paper is devoted to the study of weak metacirculants with odd prime power order. We first prove that a weak metacirculant of odd prime power order is a metacir...

This paper deals with the determination of the automorphism group of the metacyclic p-groups, P (p,m), given by the presentation P (p,m) = 〈x, y|xpm = 1, y = 1, yxy−1 = xp+1〉 (1) where p is an odd prime number and m > 1. We will show that Aut(P ) has a unique Sylow p-subgroup, Sp, and that in fact

Transmission of leishmaniasis is effected by a specific developmental stage, the metacyclic promastigote. The precursors of metacyclic promastigotes were a distinct subpopulation of parasites, identified for the first time as a new stage in the life-cycle and named leptomonad promastigotes. Microdissection of infected sandflies into 4 midgut regions and foregut allowed precursor-product relatio...