A comparison of Chehata’s and Clifford’s ordinally simple ordered groups
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- Proc. Amer. Math. Soc. 79 (1980), 512-514 Request permission
Abstract:
Chehata and Clifford gave the two most well-known examples of ordinally simple ordered groups. Chehata’s example is also algebraically simple. These two examples are shown to be similar. Clifford’s ordered group is shown to have a nonabelian algebraically simple subgroup.References
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- A. H. Clifford, A noncommutative ordinally simple linearly ordered group, Proc. Amer. Math. Soc. 2 (1952), 902–903. MR 45739, DOI 10.1090/S0002-9939-1951-0045739-4
- Vlastimil Dlab, On a family of simple ordered groups, J. Austral. Math. Soc. 8 (1968), 591–608. MR 0228397, DOI 10.1017/S1446788700006261
- Graham Higman, On infinite simple permutation groups, Publ. Math. Debrecen 3 (1954), 221–226 (1955). MR 72136
- B. H. Neumann, On ordered groups, Amer. J. Math. 71 (1949), 1–18. MR 28312, DOI 10.2307/2372087
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 512-514
- MSC: Primary 06F15; Secondary 20E32
- DOI: https://doi.org/10.1090/S0002-9939-1980-0572291-5
- MathSciNet review: 572291