For any finite Galois field extension K/F, with group G = Gal (K/F), there exists an element $$\alpha \in $$ K whose orbit $$G\cdot\alpha$$ forms F-basis of K. Such an $$\alpha$$ is called a normal element, and a normal basis. We introduce probabilistic algorithm for testing whether given \in$$ K normal, when G is either abelian or metacyclic group. The is based on the fact that deciding ...

Szasz [l ] has recently shown that a group is cyclic if and only if it satisfies condition (A) below. (A) Every cyclic subgroup of the group is for some positive integer k the subgroup generated by the £th powers of the elements of the group. We shall extend this idea here to show that a metacyclic group whose commutator subgroup has order relatively prime to its index is characterized as a sol...

The obligate intracellular protozoan, Leishmania infantum chagasi (Lic) is the causative agent of visceral leishmaniasis in South America. The flagellated promastigote life stage of the parasite undergoes receptor-mediated phagocytosis by macrophages. This process is followed by a transient delay in phagolysosome maturation that allows for conversion into the amastigotes, a stage that is resist...

A member of the Trypanosoma cruzi gp82 family, expressed on metacyclic trypomastigote surface and identified by monoclonal antibody (MAb) 3F6, plays a key role in host cell invasion. Apart from the gp82 defined by MAb 3F6, no information is available on members of this protein family. From cDNA clones encoding gp82 proteins sharing 59.1% sequence identity, we produced the recombinant proteins J...

Groups of cattle were inoculated intravenously with cloned populations of bloodstream forms of Trypanosoma brucei or Trypanosoma congolense. All five steers infected with T. brucei ILTat 2.1 and six of the eight steers infected with T. congolense IL 13-E14 became aparasitemic within 16 and 32 weeks postinfection, respectively. Examination of sera from animals infected with T. brucei by indirect...

The in vitro metacyclogenesis of a visceral (VL) and cutaneous (CL) human strain of Leishmania infantum was monitored in order to find out the kinetics of this process and the in vitro infective capacity for macrophages of the metacyclic promastigotes developed. To identify, enumerate, and separate the metacyclic population, the complement-dependent lysis by normal serum and the agglutination b...

For a number field k, let k1 denote its Hilbert 2-class field, and put k2 = (k1)1. We will determine all imaginary quadratic number fields k such that G = Gal(k2/k) is abelian or metacyclic, and we will give G in terms of generators and relations.