We join Hurwitz space constructions and the universal Frattini cover of a nite group The goal is to form and apply generalizations of the towers X p X p X p of modular curves This generalization relies on the appearance of the dihedral group Dp and its companion group Zp f g in the theory of modular curves We replace Dp by any nite group G and p by any prime dividing the order of G The replacem...

In this note we characterize all subalgebras and homomorphic images of the free cyclic Heyting algebra, also known as the RiegerNishimura lattice N . Consequently, we prove that every subalgebra of N is projective, that a finite Heyting algebra is a subalgebra of N iff it is projective, and characterize projective homomorphic images of N . The atoms and co-atoms of the lattice of all subalgebra...

Given a finite group G, let PG(s) be the probability that s randomly chosen elements generate G, and let H be a finite group with PG(s) = PH(s). We show that if the nonabelian composition factors of G and H are PSL(2, p) for some non-Mersenne prime p ≥ 5, then G and H have the same non-Frattini chief factors. Mathematics Subject Classification (2010). 20D06.