Let G be a finite group. The prime degree graph of G, denoted by D (G), is an undirected graph whose vertex set is r (G) and there is an edge between two distinct primes p and q if and only if pq divides some irreducible character degree of G. In general, it seems that the prime graphs contain many edges and thus they should have many triangles, so one of the cases that would be interesting is to consider those finite groups whose prime degree graphs have a small number of triangles. In this paper we consider the case where for a nonsolvable group G, D (G) is a connected graph which has only one triangle and four vertices.

We establish the existence of two rigid triples of conjugacy classes in the algebraic group G2 in characteristic 5, complementing results of the second author with Liebeck and Marion. As a corollary, the finite groups G2(5n) are not (2; 4; 5)-generated, conrming a conjecture of Marion in this case.

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric trian-gle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T1-separated and generally, non-Hausdor .

The purpose of the article is to demonstrate that the linking chain between Rabe'ah Adviah and Rabe'ah Bintal Ka'b is love, so that love ties them up in a more complicated and more profound way. Then according to the holographic theory, it is explained that basically there is no difference between mystical love and virtual love because in the holographic world, reality and virtuality end up to monism. Thereafter, from the intertexuality point of view, the relation between existing world of Rabe'ah Adviah and Rabe'ah Bintal Ka'b is examined and in the end, by accounting for the similarities of their existing world, the article concludes that Rabe'ah Adviah is a mirror to Rabe'ah Bintal Ka'b.