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ON THE SUBGROUP SEPARABILITY OF THE FUNDAMENTAL GROUP OF A FINITE GRAPH OF GROUPS

ON THE SUBGROUP SEPARABILITY OF THE FUNDAMENTAL GROUP OF A FINITE GRAPH OF GROUPS D E M O N S T R A T E MATHEMATICAVol. XXIXNo 11996E. Rapt is, D. VarsosON T H E S U B G R O U P S E P A R A B I L I T YOF T H E F U N D A M E N T A L G R O U POF A F I N I T E G R A P H OF G R O U P SIntroductionA group G is called subgroup separable ( S S ) if for every finitely generated (f.g.) subgroup H and every element g € G\H, there is a finite indexsubgroup L, which contains H but g L. Equivalently the group G is SSif there is a homomorphism of G onto a finite group such that the image ofg remains outside the image of H. Evidently a SS group is residually finiteCRT), that is for 1 ^ g 6 G there is a finite index subgroup L (L <j G)such that g & L.Just as the study of f.g. 7ZT groups leads to the solution of the wordproblem, the study of f.g. SS groups leads to the solution of the generalizedword problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON THE SUBGROUP SEPARABILITY OF THE FUNDAMENTAL GROUP OF A FINITE GRAPH OF GROUPS

Demonstratio Mathematica , Volume 29 (1): 10 – Jan 1, 1996

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Publisher
de Gruyter
Copyright
© by E. Raptis
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1996-0108
Publisher site
See Article on Publisher Site

Abstract

D E M O N S T R A T E MATHEMATICAVol. XXIXNo 11996E. Rapt is, D. VarsosON T H E S U B G R O U P S E P A R A B I L I T YOF T H E F U N D A M E N T A L G R O U POF A F I N I T E G R A P H OF G R O U P SIntroductionA group G is called subgroup separable ( S S ) if for every finitely generated (f.g.) subgroup H and every element g € G\H, there is a finite indexsubgroup L, which contains H but g L. Equivalently the group G is SSif there is a homomorphism of G onto a finite group such that the image ofg remains outside the image of H. Evidently a SS group is residually finiteCRT), that is for 1 ^ g 6 G there is a finite index subgroup L (L <j G)such that g & L.Just as the study of f.g. 7ZT groups leads to the solution of the wordproblem, the study of f.g. SS groups leads to the solution of the generalizedword problem.

Journal

Demonstratio Mathematicade Gruyter

Published: Jan 1, 1996

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