A shortest single axiom with neutral element for commutative Moufang loops of exponent 3
نویسنده
چکیده
In this brief note, we exhibit a shortest single product and neutral element axiom for commutative Moufang loops of exponent 3 that was found with the aid of the automated theorem-prover Prover9.
منابع مشابه
Primary Decompositions in Varieties of Commutative Diassociative Loops
The decomposition theorem for torsion abelian groups holds analogously for torsion commutative diassociative loops. With this theorem in mind, we investigate commutative diassociative loops satisfying the additional condition (trivially satisfied in the abelian group case) that all nth powers are central, for a fixed n. For n = 2, we get precisely commutative C loops. For n = 3, a prominent var...
متن کاملThe Structure of Automorphic Loops
Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes, for instance, groups and commutative Moufang loops. We study uniquely 2-divisible automorphic loops, particularly automorphic loops of odd order, from the point of view of the associated Bruck loops (motivated by Glauberman’s work on uniquely 2-divisible Moufang loops) and the associated L...
متن کاملThe commutative Moufang loops with maximum conditions for subloops
It is proved that the maximum condition for subloops in a commutative Moufang loop Q is equivalent with the conditions of finite generating of different subloops of the loop Q and different subgroups of the multiplication group of the loop Q. An analogue equivalence is set for the commutative Moufang ZA-loops. Classification: 20N05
متن کاملThe Structure of Free Automorphic Moufang Loops
We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.
متن کاملA Scoop from Groups: Equational Foundations for Loops
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain “group-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 40 شماره
صفحات -
تاریخ انتشار 2008