某些陀螺群的正常亚陀螺群

Q3 Mathematics Quasigroups and Related Systems Pub Date : 2021-06-05 DOI:10.56415/qrs.v30.09

Mahdavi Soheila, Ashrafi Ali-Reza, Salahshour Mohammad A.

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引用次数: 1

摘要

假设(T;*)是一个具有左单位元的群，使得2t的每个元素都有一个左逆。那么当且仅当(i)存在一个函数gyr: T x T -Aut(T)使得对于所有a;b;c2t, a * (b * c) = (a * b)gyr[一个;c, where gyr[a];B]c = gyr(a;b) (c);(ii)所有a;b 2 T, gyr[a;B] = gyr[a] ?b;b]。本文研究了某些陀螺群的正规子陀螺群的结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Normal subgyrogroups of certain gyrogroups

Suppose that (T;*) is a groupoid with a left identity such that each element a 2 T has a left inverse. Then T is called a gyrogroup if and only if (i) there exists a function gyr : T x T -Aut(T) such that for all a; b; c 2 T, a * (b * c) = (a * b) ? gyr[a; b]c, where gyr[a; b]c = gyr(a; b)(c); and (ii) for all a; b 2 T, gyr[a; b] = gyr[a ? b; b]. In this paper, the structure of normal subgyrogroups of certain gyrogroups are investigated.

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