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Two questions on semigroup laws

Published online by Cambridge University Press:  17 April 2009

O. Macedońska
O. Macedońska
Affiliation:
Institute of Mathematics, Silesian Technical University, ul. Kaszubska 23, 44–100 Gliwice, Poland, e-mail: olga@zeus.polsl.gliwice.pl
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Abstract

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B.H. Neumann recently proved some implications for semigroup laws in groups. This may help in the solution of a problem posed by G.M. Bergman in 1981.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 431 - 437
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Burns, R.G., Macedońska, O. and Medvedev, Y.,, ‘Groups satisfying semigroup laws, and nilpotent-by-Burnside varieties’, J. Algebra 195 (1997), 510–525.CrossRefGoogle Scholar
[2]Bergman, G.M., ‘Hyperidentities of groups and semigroups’, Aequationes Math. 23 (1981), 50–65.CrossRefGoogle Scholar
[3]Bergman, G.M., ‘Questions in algebra’, (preprint, Berkeley, U.C. 1986).Google Scholar
[4]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Math. Surveys 7 (Amer. Math. Soc., Providence R.I., 1964).Google Scholar
[5]Krempa, J. and Macadońska, O., ‘On identities of cancellative semigroups’, Contemp. Mathem. 131 (1992), 125–133.CrossRefGoogle Scholar
[6]Lewin, J. and Lewin, T., ‘Semigroup laws in varieties of soluble groups’, Proc. Cambridge Philos. Soc. 65 (1969), 1–9.CrossRefGoogle Scholar
[7]Macedońska, O., ‘On cancellative congruences for semigroups’, Zeszyty Nauk. Politech. Slaskiej Mat.-Fiz. 84 (1999), 171–176.Google Scholar
[8]Macedońska, O. and Żabka, M., ‘On equivalence of semigroup identities’, Math. Scand. 88 (2001), 161–181.CrossRefGoogle Scholar
[9]Malcev, A.I., ‘Nilpotent semigroups’, Ivanov. Gos. Ped. Inst. Uc. Zap. Fiz. Mat. Nauki 4 (1953), 107–111.Google Scholar
[10]Neumann, B.H., ‘Some semigroup laws in groups’, Canad. Math. Bull. 44 (2001), 93–96.CrossRefGoogle Scholar
[11]Neumann, H., Varieties of groups (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[12]Shirshov, A.I., ‘On some positively defined varieties of groups’, Siberian Math. J. (1959), 165–178.Google Scholar