Geodesic
On the group ${GL}(2,R[X])$
The electronic journal of linear algebra, Tome 7 (2000), pp. 59-72.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Suppose that G is an arbitrary group and S is its subset such that S $\Gamma 1$ = S. Let $gr(S)$ be the subgroup of G generated by S. Denote by l S (g) the length of element g $2 gr(S)$ relative to the set S. Let V be a finite subset of a free group F of countable rank and let the verbal subgroup V (F ) be a proper subgroup of F . For an arbitrary group G, denote by V (G) the set of values in the group G of all the words from the set V . The present paper establishes the infinity of the set fl S (g); g 2 V (G)g, where $G = GL(2; R[x])$, S = V (G) [ V (G) $\Gamma 1$ for an arbitrary field R.
Classification : 20E06, 20F22
Keywords: verbal subgroup, width of verbal subgroup, pseudocharacter 
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     title = {On the group ${GL}(2,R[X])$},
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Fajziev, Valerij. On the group ${GL}(2,R[X])$. The electronic journal of linear algebra, Tome 7 (2000), pp. 59-72. http://geodesic.mathdoc.fr/item/ELA_2000__7__a8/