Abstract
Several authors (Hausmann and Ore [87], Griffin [86], Murdoch [92], [93] and others) have discussed coset expansion for quasigroups. We shall treat only loops. The loop G is said to have a right coset expansion modulo its subloop H provided the right cosets Hx partition G. Since each x of G lies in at least one right coset, namely Hx, the condition for a right coset expansion is: If y ∈ H x, then Hy = Hx.
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© 1971 Springer-Verlag Berlin Heidelberg
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Bruck, R.H. (1971). Lagrange’s Theorem for Loops. In: A Survey of Binary Systems. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol NF 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43119-1_5
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DOI: https://doi.org/10.1007/978-3-662-43119-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-42837-5
Online ISBN: 978-3-662-43119-1
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