Add to ORKGsummary:Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i,j,k\in\{-1,\,1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above 8 multiplications to each quarter $(G\times\{i\})\times(G\times\{j\})$, for $i,j\in C_2$. If the resulting quasigroup is a Bol loop, it is Moufang. When $G$ is nonabelian then exactly four assignments yield Moufang loops that are not associative; all (anti)isomorphic, known as loops $M(G,2)$
summary:A loop $Q$ is said to be left conjugacy closed (LCC) if the set $\{L_x; x \in Q\}$ is closed...
In this thesis I shall be exploring the normal and characteristic structure of quasigroups and loops...
summary:We investigate loops which can be written as the semidirect product of a loop and a group, a...
Abstract. Let G be a finite group and C2 the cyclic group of order 2. Consider the 8 multiplicative ...
summary:Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicati...
summary:We contrast the simple proof that a quasigroup which satisfies the Moufang identity $(x\cdot...
summary:Given a uniquely 2-divisible group $G$, we study a commutative loop $(G,\circ)$ which arises...
Abstract. A loop identity is of Bol-Moufang type if two of its three variables occur once on each si...
summary:If $(G,\cdot )$ is a group, and the operation $(\ast )$ is defined by $x\ast y=x\cdot y^{-1}...
summary:In a series of papers from the 1940's and 1950's, R.H. Bruck and L.J. Paige developed a pr...
AbstractOne of the most interesting constructions of nonassociative Moufang loops is the constructio...
Loops are nonassociative generalization of groups. Moufang loops are characterized by the identity (...
Abstract. Groups are usually axiomatized as algebras with an associative binary oper-ation, a two-si...
summary:This paper completely solves the isomorphism problem for Moufang loops $Q = GC$ where $G\unl...
Abstract. (Left) Bol loops are usually introduced as loops in which (left) Bol condition is satisfie...
summary:A loop $Q$ is said to be left conjugacy closed (LCC) if the set $\{L_x; x \in Q\}$ is closed...
In this thesis I shall be exploring the normal and characteristic structure of quasigroups and loops...
summary:We investigate loops which can be written as the semidirect product of a loop and a group, a...
Abstract. Let G be a finite group and C2 the cyclic group of order 2. Consider the 8 multiplicative ...
summary:Let $G$ be a finite group and $C_2$ the cyclic group of order 2. Consider the 8 multiplicati...
summary:We contrast the simple proof that a quasigroup which satisfies the Moufang identity $(x\cdot...
summary:Given a uniquely 2-divisible group $G$, we study a commutative loop $(G,\circ)$ which arises...
Abstract. A loop identity is of Bol-Moufang type if two of its three variables occur once on each si...
summary:If $(G,\cdot )$ is a group, and the operation $(\ast )$ is defined by $x\ast y=x\cdot y^{-1}...
summary:In a series of papers from the 1940's and 1950's, R.H. Bruck and L.J. Paige developed a pr...
AbstractOne of the most interesting constructions of nonassociative Moufang loops is the constructio...
Loops are nonassociative generalization of groups. Moufang loops are characterized by the identity (...
Abstract. Groups are usually axiomatized as algebras with an associative binary oper-ation, a two-si...
summary:This paper completely solves the isomorphism problem for Moufang loops $Q = GC$ where $G\unl...
Abstract. (Left) Bol loops are usually introduced as loops in which (left) Bol condition is satisfie...
summary:A loop $Q$ is said to be left conjugacy closed (LCC) if the set $\{L_x; x \in Q\}$ is closed...
In this thesis I shall be exploring the normal and characteristic structure of quasigroups and loops...
summary:We investigate loops which can be written as the semidirect product of a loop and a group, a...
