the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.

Using Galois theory, we explicitly construct (in all complex dimensions $$g\ge 2$$ ) an infinite family of simple $$g$$ -dimensional tori $$T$$ that enjoy the following properties: $$\bullet$$ Picard number is $$0;$$ in particular, algebraic dimension $$0$$ ; if $$T^\vee$$ dual , then $$\mathrm{Hom}(T,T^\vee)=\{0\}$$ automorphism group $$\mathrm{Aut}(T)$$ isomorphic to $$\{\pm 1\} \times \mathb...