In this paper, a classification of the regular embeddings of Kn,n, where n = 2e is a power of two, is completed. The number of such regular maps is one or two for e = 1, 2, respectively. For e ≥ 3 there are 2e−2 + 4 regular embeddings of K2e,2e . The method is based on classification of groups G which factorise as a product of two cyclic groups G = XY of order n such that the cyclic factors are...

Leishmania chagasi causes visceral leishmaniasis, a potentially fatal disease of humans. Within the sand fly vector, L. chagasi replicates as promastigotes which undergo complex changes in morphology as they progress from early stage procyclic promastigotes, to intermediate stage leptomonad and nectomonad promastigotes, and ultimately to terminal stage metacyclic promastigotes that are highly i...

Suppose that a finite solvable group G acts faithfully, irreducibly and quasi-primitively on vector space V, is not metacyclic. Then always has regular orbit V except for few “small” cases. We completely classify these cases in this paper.

In this paper, we classify finite quasiprimitive permutation groups with a metacyclic transitive subgroup, solving problem initiated by Wielandt in 1949. It also involves the classification of factorizations almost simple factor.

Intradermal inoculation of metacyclic forms of Trypanosoma congolense propagated in vitro caused skin reactions in goats similar to the local skin reaction (chancre) induced by the bite of an infected tsetse fly. The onset, size and duration of these local skin reactions were dose-dependent. Whereas one cultured metacyclic T. congolense was sufficient to cause a local skin reaction in a goat, o...

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...