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Residuals of the Join of Ascendant Subgroups
Published online by Cambridge University Press: 20 November 2018
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If G is a group, then we say H is an ascendant subgroup of G, and write H asc G, if there exists a sequence of subgroups (Gα)α ≦ ρ where ρ is some ordinal number, such that G0 = H, Gp = G, Gρ ⊲ Gα+1 for all α < ρ and G ƛ = ⋂ {Gα α| α ⊲ ƛ} for all limit ordinals λ ≦ ρ. (Gα) α ≦ ρ is said to be an ascending series from H to G.
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- Copyright © Canadian Mathematical Society 1977
References
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