论文标题
自动循环的半同态
Half-isomorphisms of automorphic loops
论文作者
论文摘要
自动循环是所有内部映射都是自动形态的循环。这些循环包括组和交换性穆法循环。乘法系统$ g $和$ k $之间的半同态$ f：g \ longrightArrow k $是$ g $从$ k $到$ k $的两次循环，因此$ f（ab）\ in \ {f（a）f（a）f（b），f（b）f（b）f（a）f（a）f（a）\} $ in g $ in g $ in g $ in g $。当同构是同构或抗同态时，半同态是微不足道的。考虑自动循环的类别，以便方程$ x \ cdot（x \ cdot y）=（y \ cdot x）\ cdot x $等于$ x \ cdot y = y \ cdot x $。在这里，我们表明，这类循环包括奇数订单的自动循环和独特的$ 2 $ - 可见。此外，我们证明该类别的循环之间的每个半态性都是微不足道的。
Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes groups and commutative Moufang loops. A half-isomorphism $f : G \longrightarrow K$ between multiplicative systems $G$ and $K$ is a bijection from $G$ onto $K$ such that $f(ab)\in\{f(a)f(b), f(b)f(a)\}$ for any $a,b\in G$. A half-isomorphism is trivial when it is either an isomorphism or an anti-isomorphism. Consider the class of automorphic loops such that the equation $x\cdot(x\cdot y) = (y\cdot x)\cdot x $ is equivalent to $x\cdot y = y\cdot x$. Here we show that this class of loops includes automorphic loops of odd order and uniquely $2$-divisible. Furthermore, we prove that every half-isomorphism between loops in that class is trivial.
