TY - JOUR
T1 - Elementary group equivalence with the integral length function
AU - Myasnikov, A. G.
AU - Remeslennikov, V. N.
PY - 1986
Y1 - 1986
N2 - The paper determines criteria of elementary equivalence for some classes of free groups with operators and free products with the length function. The case of a group with operators admitting rational coordinatizati0n with a finite basis is completely analyzed. They are polycyclic, solvable groups of finite rank without torsion, and Chernikov groups. The concept of t0-isomorphism of groups intermediate between elementary equivalence and isomorphism is important for the aspects of elementary equivalence of groups with operators and free product. It is proved that to-isomorphism of arbitrary groups of operators is followed by the elementary equivalence of the respective free operator groups (free products) with length function.
AB - The paper determines criteria of elementary equivalence for some classes of free groups with operators and free products with the length function. The case of a group with operators admitting rational coordinatizati0n with a finite basis is completely analyzed. They are polycyclic, solvable groups of finite rank without torsion, and Chernikov groups. The concept of t0-isomorphism of groups intermediate between elementary equivalence and isomorphism is important for the aspects of elementary equivalence of groups with operators and free product. It is proved that to-isomorphism of arbitrary groups of operators is followed by the elementary equivalence of the respective free operator groups (free products) with length function.
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U2 - 10.1215/ijm/1256044642
DO - 10.1215/ijm/1256044642
M3 - Article
AN - SCOPUS:84972571979
SN - 0019-2082
VL - 30
SP - 335
EP - 354
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 2
ER -