On a conjecture of B. Hartley and
some related problems

J. Krempa

In this note we are going to survey some questions and results related to a conjecture of Brian Hartley about identities for groups of units in group algebras.

1. A.A. Bovdi Group rings ,addr Kiev- 1988Russian

2. A.A. Bovdi Free subgroups of the group of units in group algebras// Publ. Math. Debrecen V.49-1996 N. 1-2 p.157-166

3. Y. Billig, D. Riley & V. Tasić Non-matrix varieties and nil-generated algebras whose units satisfy a group identity// preprint- 1996

4. A. Giambruno, E. Jespers & A. Valenti Group identities on units of rings// Arch. Math. V.63-1994 p. 291-296

5. A. Giambruno, S.K. Sehgal & A. Valenti Group algebras whose units satisfy a group identity// Proc. AMS

6. J.Z. Gonçalves. Free subgroups of units in group rings. Canad. Math. Bull., 27 (1984), 309–312. 7. J.Z. Gonçalves & D.S. Passman. Construction of free subgroups in the group of units of modular group algebras. Comm. Alg. (to appear). 8. B. Hartley & P.F. Pickel Free subgroups in the unit group of integral group rings// Canad. J. Math. V.32-1980 p. 1342-1352

9. G. Karpilovsky Unit groups of group rings , Longman,addr Essex- 1989

10. R.C. Lyndon & P.E. Schupp Combinatorial group theory, Springer-Verlag,addr Berlin -1977

11. Z.S. Marciniak & S.K. Sehgal Constructing free subgroups of integral group ring units// Proc. AMS

12. H. Nagao On GL$_2${K[x]}.// J. Inst. Polytech. Osaka City Univ., ser. A10 -- 1959 p. 117--121

13. D.S. Passman The algebraic structure of group rings, Wiley-Interscience Publications,addr New York -1977

14. D.S. Passman Group algebras whose units satisfy a group identity II// Proc. AMS

15. S.K. Sehgal Topics in group rings, Marcel Dekker Inc.,addr New York- 1978

16. J. Tits Free subgroups in linear group// J. of Algebra V. 20-1972 p. 250-270

17. B.A.F. Wehrfritz Infinite linear groups , Springer-verlag,addr Berlin -- 1973

	On a conjecture of B. Hartley and some related problems
Author	J. Krempa jkrempa@mimuw.edu.pl Institute of Mathematics, Warsaw Universityul. Banacha 2, 02-097 Warszawa, Poland
Abstract	In this note we are going to survey some questions and results related to a conjecture of Brian Hartley about identities for groups of units in group algebras.
Keywords	Brian Hartley conjecture, identities, groups of units, group algebras
DOI	doi:10.30970/ms.8.2.171-175
Reference	1. A.A. Bovdi Group rings ,addr Kiev- 1988Russian 2. A.A. Bovdi Free subgroups of the group of units in group algebras// Publ. Math. Debrecen V.49-1996 N. 1-2 p.157-166 3. Y. Billig, D. Riley & V. Tasić Non-matrix varieties and nil-generated algebras whose units satisfy a group identity// preprint- 1996 4. A. Giambruno, E. Jespers & A. Valenti Group identities on units of rings// Arch. Math. V.63-1994 p. 291-296 5. A. Giambruno, S.K. Sehgal & A. Valenti Group algebras whose units satisfy a group identity// Proc. AMS 6. J.Z. Gonçalves. Free subgroups of units in group rings. Canad. Math. Bull., 27 (1984), 309–312. 7. J.Z. Gonçalves & D.S. Passman. Construction of free subgroups in the group of units of modular group algebras. Comm. Alg. (to appear). 8. B. Hartley & P.F. Pickel Free subgroups in the unit group of integral group rings// Canad. J. Math. V.32-1980 p. 1342-1352 9. G. Karpilovsky Unit groups of group rings , Longman,addr Essex- 1989 10. R.C. Lyndon & P.E. Schupp Combinatorial group theory, Springer-Verlag,addr Berlin -1977 11. Z.S. Marciniak & S.K. Sehgal Constructing free subgroups of integral group ring units// Proc. AMS 12. H. Nagao On GL$_2${K[x]}.// J. Inst. Polytech. Osaka City Univ., ser. A10 -- 1959 p. 117--121 13. D.S. Passman The algebraic structure of group rings, Wiley-Interscience Publications,addr New York -1977 14. D.S. Passman Group algebras whose units satisfy a group identity II// Proc. AMS 15. S.K. Sehgal Topics in group rings, Marcel Dekker Inc.,addr New York- 1978 16. J. Tits Free subgroups in linear group// J. of Algebra V. 20-1972 p. 250-270 17. B.A.F. Wehrfritz Infinite linear groups , Springer-verlag,addr Berlin -- 1973
Pages	171-175
Volume	8
Issue	2
Year	1997
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On a conjecture of B. Hartley and some related problems