The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On the uniqueness of loops M ( G , 2 )

A class of Bol loops with a subgroup of index two

Petr Vojtěchovský (2004)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let G be a finite group and C 2 the cyclic group of order 2 . Consider the 8 multiplicative operations ( x , y ) ( x i y j ) k , where i , j , k { - 1 , 1 } . Define a new multiplication on G × C 2 by assigning one of the above 8 multiplications to each quarter ( G × { i } ) × ( G × { j } ) , for i , j C 2 . We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojtěchovsk’y: On the uniqueness of loops M ( G , 2 ) .

Right division in Moufang loops

Maria de Lourdes M. Giuliani, Kenneth Walter Johnson (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If ( G , · ) is a group, and the operation ( * ) is defined by x * y = x · y - 1 then by direct verification ( G , * ) is a quasigroup which satisfies the identity ( x * y ) * ( z * y ) = x * z . Conversely, if one starts with a quasigroup satisfying the latter identity the group ( G , · ) can be constructed, so that in effect ( G , · ) is determined by its right division operation. Here the analogous situation is examined for a Moufang loop. Subtleties arise which are not present in the group case since there is a choice of defining identities and the identities...