Gröbner–Shirshov Basis for HNN Extensions of Groups and for the Alternating Group

Abstract

In this article, we generalize the Shirshov's Composition Lemma by replacing the monomial order for others. By using Gröbner–Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained.

Key Words:

• Alternating group
• Gröbner–Shirshov basis
• HNN extension
• Normal form

2000 Mathematics Subject Classification:

• 20E06
• 16S15
• 13P10

ACKNOWLEDGMENT

The authors would like to express their deepest gratitude to Professor L. A. Bokut for his kind guidance, useful discussions, and enthusiastic encouragement during his visit to the South China Normal University.

The research is supported by the National Natural Science Foundation of China (Grant No. 10771077) and the Natural Science Foundation of Guangdong Province (Grant No. 021073; 06025062).

Notes

Communicated by V. A. Artamonov.