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Residuals of the Join of Ascendant Subgroups

Published online by Cambridge University Press:  20 November 2018

Jennifer Whitehead
Jennifer Whitehead*
Affiliation:
University of Warwick, Coventry, England; Texas A & M University. College Station, Texas
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1066 - 1068
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Hartley, B. and Peng, T. A., Subnormality, ascendancy and the minimal condition, J. Algebra 41 (1976), 58–78.Google Scholar
2. Robinson, D. J. S., On the theory of subnormal subgroups, Math. Z. 89 (1965), 30–51.Google Scholar
3. Robinson, D. J. S. Finiteness conditions and generalized soluble groups, Part 1 (Springer, Berlin/Heidelberg/ New York, 1972).Google Scholar
4. Wielandt, H., Vertauschbare nachinvariante Untergruppen, Abh. Math. Sem. Univ. Hamburg 21 (1957), 55–62.Google Scholar