Abstract
The notion of a relative Grobner-Shirshov basis for algebras and groups is introduced. The relative composition lemma and relative (composition-)diamond lemma are established. In particular, it is shown that the relative normal forms of certain groups arising from Malcev's embedding problem are the irreducible nor- mal forms of these groups with respect to their relative Grobner-Shirshov bases. Other examples of such groups are given by showing that any group G in a Tits sys- tem (G, B, N, S )h as ar elative (B-)Grobner-Shirshov basis such that the irreducible words are the Bruhat words of G.
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