On the number of squares in a group
Author:
Ludomir Newelski
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
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Abstract | References | Similar Articles | Additional Information
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.
- C. C. Chang and H. J. Keisler, Model theory, 2nd ed., North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Studies in Logic and the Foundations of Mathematics, 73. 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 https://doi.org/10.1016/0003-4843%2871%2990015-5 ---, Classification theory, North-Holland, Amsterdam, 1978.
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Article copyright:
© Copyright 1987
American Mathematical Society
