Coincident pairs of continuous sections in profinite groups
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- by H. Appelgate and H. Onishi
- Proc. Amer. Math. Soc. 63 (1977), 217-220
- DOI: https://doi.org/10.1090/S0002-9939-1977-0442099-X
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Abstract:
Given a profinite group G and a closed subgroup H, we show there exist continuous sections $s:{(G/H)_1} \to G$ and $s’:{(G/H)_r} \to G$ of the projections $G \to {(G/H)_1}$ and $G \to {(G/H)_r}$ onto the left and right coset spaces, respectively, such that ${\text {im}}(s) = {\text {im}}(s’)$.References
- Oystein Ore, On coset representatives in groups, Proc. Amer. Math. Soc. 9 (1958), 665–670. MR 100639, DOI 10.1090/S0002-9939-1958-0100639-2
- Herbert John Ryser, Combinatorial mathematics, The Carus Mathematical Monographs, No. 14, Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York, 1963. MR 0150048 J.-P. Serre, Cohomologie galoisienne, Lecture Notes in Math., vol. 5, Springer-Verlag, Berlin and New York, 1964. MR 31 #4785.
Bibliographic Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 217-220
- MSC: Primary 20F20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0442099-X
- MathSciNet review: 0442099