Page 1 Next

Displaying 1 – 20 of 324

Showing per page

A class of commutative loops with metacyclic inner mapping groups

Aleš Drápal (2008)

Commentationes Mathematicae Universitatis Carolinae

We investigate loops defined upon the product m × k by the formula ( a , i ) ( b , j ) = ( ( a + b ) / ( 1 + t f i ( 0 ) f j ( 0 ) ) , i + j ) , where f ( x ) = ( s x + 1 ) / ( t x + 1 ) , for appropriate parameters s , t m * . Each such loop is coupled to a 2-cocycle (in the group-theoretical sense) and this connection makes it possible to prove that the loop possesses a metacyclic inner mapping group. If s = 1 , then the loop is an A-loop. Questions of isotopism and isomorphism are considered in detail.

A computer algebra solution to a problem in finite groups.

Gert-Martin Greuel (2003)

Revista Matemática Iberoamericana

We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.

Currently displaying 1 – 20 of 324

Page 1 Next