Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed isomorphic to a normal (resp. characteris...

This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....

Reversible logic plays a fundamental role both in ultra-low power electronics and in quantum computing. It is therefore important to have an insight into the structure of the group formed by the reversible logic gates and their cascading into reversible circuits. Such insight is gained from constructing chains of maximal subgroups. The subgroup of control gates plays a prominent role, as it is ...

Let p be any prime. P n a Sylow -subgroup of the symmetric group S . ϕ and ψ linear characters let N normaliser in In this article we show that inductions to are equal if, only –conjugate. This is an analogue for groups result Navarro -solvable groups.

Let [Formula: see text] be a finite group and fixed prime divisor of text]. We prove that if every maximal subgroup is nilpotent, or normal, has text]-order, then (1) solvable; (2) Sylow tower; (3) there exists at most one such neither text]-nilpotent nor text]-closed.