A product variety of groups with distributive lattice
Author:
L. F. Harris
Journal:
Proc. Amer. Math. Soc. 43 (1974), 53-56
MSC:
Primary 20E10
DOI:
https://doi.org/10.1090/S0002-9939-1974-0332986-2
MathSciNet review:
0332986
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Abstract | References | Similar Articles | Additional Information
Abstract: By a variety of -groups is meant a locally finite variety of groups whose nilpotent groups are abelian. It is shown that if
is a variety of
-groups and
is a locally finite variety whose lattice of subvarieties is distributive and the exponents of
and
are coprime, then the lattice of subvarieties of the product variety
is distributive.
- [1] M. S. Brooks, On lattices of varieties of metabelian groups, J. Austral. Math. Soc. 12 (1971), 161–166. MR 0294456
- [2] R. M. Bryant and L. G. Kovács, The skeleton of a variety of groups, Bull. Austral. Math. Soc. 6 (1972), 357–378. MR 306324, https://doi.org/10.1017/S0004972700044634
- [3] R. A. Bryce, Metabelian groups and varieties, Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 281–355. MR 265440, https://doi.org/10.1098/rsta.1970.0008
- [4] John Cossey, Critical groups and the lattice of varieties, Proc. Amer. Math. Soc. 20 (1969), 217–221. MR 232824, https://doi.org/10.1090/S0002-9939-1969-0232824-0
- [5] Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- [6] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- [7] Hanna Neumann, Varieties of groups, Springer-Verlag New York, Inc., New York, 1967. MR 0215899
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1974-0332986-2
Article copyright:
© Copyright 1974
American Mathematical Society