On the number of squares in a group
HTML articles powered by AMS MathViewer
- by Ludomir Newelski PDF
- Proc. Amer. Math. Soc. 99 (1987), 213-218 Request permission
Abstract:
We show that there is a connection between the number of squares in a group and the cardinality of the group. For example, if a group has countably many squares and ${x^2} = e$ implies $x = e$, then its cardinality is bounded by ${2^{{\aleph _0}}}$ and this bound can be obtained.References
- C. C. Chang and H. J. Keisler, Model theory, 2nd ed., Studies in Logic and the Foundations of Mathematics, vol. 73, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0532927
- Saharon Shelah, Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Ann. Math. Logic 3 (1971), no. 3, 271–362. MR 317926, DOI 10.1016/0003-4843(71)90015-5 —, Classification theory, North-Holland, Amsterdam, 1978.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 213-218
- MSC: Primary 20A15; Secondary 03C45, 20E99
- DOI: https://doi.org/10.1090/S0002-9939-1987-0870773-6
- MathSciNet review: 870773