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.

A new family of methods involving complex coefficients for the numerical integration differential equations is presented and analyzed. They are constructed as linear combinations symmetric-conjugate compositions obtained from a basic time-symmetric integrator order 2n (n≥1). The integrators 2(n+k), k=1,2,…, preserve time-symmetry up to 4n+3 when applied with real vector fields. If in addition s...