To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Grobner-Shirshov bases for Schreier extensions of groups

Yuqun Chen
School of Mathematical Sciences
South China Normal University


Let A, B, G be groups. G is called a Schreier extensions of A by B if A is a normal subgroup of G and G/A is isomorphic to B. In this paper, by using the Grobner-Shirshov bases, we give characterizations of the Schreier extensions of groups when the group B is presented by generators and relations. An algorithm to find the conditions of a group G to be a Schreier extension of A by B is obtained. By introducing a special well order, we obtain the structure of the Schreier extension by an HNN group.

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