On a decomposition of an element of a free metabelian group as a productof primitive elements - статья по прочим предметам

 

Тезисы:

  • Presentation of elements of a free abelian group of rank n as a product of primitive elements.
  • Then c= (a1s1...ansn) (a1t1...antn) is a product of two primitive elements.
  • So one can say about finite or infinite primitive length of given relatively free group.
  • Of a free abelian group An is primitive if and only if the vector (k1,...,kn) is unimodular.
  • Can be presented as a product of not more then two primitive elements.
  • Let G=Fn/V be a free in some variety group of rank n. An element.
  • Let An be a free abelian group of rank n with a basis a1,a2,...,an. Any element.
  • A primitive length |g|pr of an element.
  • A primitive length |G|pr of a group G is defined as.
  • If c is primitive, then it can be included into a basis c=c1,c2,...,cn of the group An. The group.
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