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On denumerable chains of infinite order

✍ Scribed by M. Iosifescu; A. Spătaru


Publisher
Springer
Year
1973
Tongue
English
Weight
802 KB
Volume
27
Category
Article
ISSN
1432-2064

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📜 SIMILAR VOLUMES


Chain Conditions for Subgroups of Infini
✍ Dae Hyun Paek 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 115 KB

A group G is said to satisfy max-∞ if each nonempty set of infinite subgroups of G has a maximal element. A group G is said to satisfy min-∞ if each nonempty set of subgroups of G with infinite index has at least one minimal element. Groups with max-∞ or min-∞ are the subject of this paper. Abelian

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We say that an ordered set P is spanned by a family %? of chains if P = (P, <) is the transitive closure of lJ{(c, < 1 C). C E U}. It is shown that there is a function h: w +w such that if P is spanned by k < o chains, then P has a finite cutset-number <h(k) (i.e. for any x E P, there is a finite se