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
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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