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.

Let $G$ be a group and $pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L_2(p^2))$, where $pin{11,13}$‎.‎

Abstract We consider the simplices $$\begin{aligned} K_n^A=\{x\in {\mathbb {R}}^{n+1}:x_1\ge x_2\ge \cdots \ge x_{n+1},x_1-x_{n+1}\le 1,\,x_1+\cdots +x_{n+1}=0\} \end{aligned}$$ K n A = {</m...

A $k$-uniform tight cycle is a hypergraph with cyclic ordering of its vertices such that edges are all the sets size $k$ formed by consecutive in ordering.We prove every red-blue edge-coloured $K_n^{(4)}$ contains red and blue vertex-disjoint together cover $n-o(n)$ vertices. Moreover, we $K_n^{(5)}$ four monochromatic cycles

A factorisation x = u 1 2 ? $x u_1 u_2 \cdots$ of an infinite word $x$ on alphabet X $X$ is called ‘monochromatic’, for a given colouring the finite words ? $X^*$ , if each i $u_i$ same colour. Wojcik and Zamboni proved that periodic only every there monochromatic . On other hand, it follows from Ramsey's theorem that, any suffix having factorisation. ‘super-monochromatic’ k n $u_{k_1} u_{k_2} ...