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On the uniqueness of loops M ( G , 2 )

Petr Vojtěchovský (2003)

Commentationes Mathematicae Universitatis Carolinae

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 . 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 ) .

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

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