论文标题
具有同构非亚伯式的有限偏斜牙套特征性的简单添加剂和圆形组
Finite skew braces with isomorphic non-abelian characteristically simple additive and circle groups
论文作者
论文摘要
偏斜的支撑是一个三重态$（a，\ cdot，\ circ）$，其中$（a，\ cdot）$和$（a，\ circ）$是群体，以至于支撑关系$ x \ circ（y \ cdot z）=（x \ circ y）在本文中，我们研究了有限的偏斜括号$（a，\ cdot，\ circ）$，达到同构，使得$（a，\ cdot）$和$（a，\ circ）$均与$ t^n $同构为$ t^n $，$ t $ t $ non-belian simple and $ n \ in \ in \ nath \ nath \ nth} $ n} $ n} $ n}。我们证明，它等于$ n+1 $顶点上未标记的有向图的数量，带有一个遥远的顶点，其基本的无向图是一棵树。特别是，它仅取决于$ n $，并且独立于$ t $。
A skew brace is a triplet $(A,\cdot,\circ)$, where $(A,\cdot)$ and $(A,\circ)$ are groups such that the brace relation $x\circ (y\cdot z) = (x\circ y)\cdot x^{-1}\cdot (x\circ z)$ holds for all $x,y,z\in A$. In this paper, we study the number of finite skew braces $(A,\cdot,\circ)$, up to isomorphism, such that $(A,\cdot)$ and $(A,\circ)$ are both isomorphic to $T^n$ with $T$ non-abelian simple and $n\in\mathbb{N}$. We prove that it is equal to the number of unlabeled directed graphs on $n+1$ vertices, with one distingusihed vertex, and whose underlying undirected graph is a tree. In particular, it depends only on $n$ and is independent of $T$.
