Some Thin Pro-p-Groups
نویسندگان
چکیده
منابع مشابه
Young Algebra Seminar 2001–2002 THIN LIE ALGEBRAS AND THIN PRO–p–GROUPS
The purpose of these notes is to give an overview on a class of (graded) Lie algebras, which satisfy certain narrowness conditions on the lattice of their homogeneous ideals. Narrowness conditions arise in the theory of p-groups and pro-p groups. In the group theoretic context, the best known condition for a group is to be of maximal class. Let p be a prime. A group G of order p is said to be a...
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In the 1970s, Isaacs conjectured that there should be a logarithmic bound for the length of solvability of a p-group G with respect to the number of different irreducible character degrees of G. So far, there are just a few partial results for this conjecture. In this note, we say that a pro-p group G has property (I) if there is a real number D = D(G) that just depends on G such that for any o...
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Let Γ be a finitely presentable pro-p group such that def(Γ) > 0. If Γ has a nontrivial finitely generated closed normal subgroup N of infinite index then def(Γ) = 1, N is a free pro-p group and Γ/N is virtually free. If π is a finitely presentable group with β (2) 1 (π) = 0 then def(π) ≤ 1, with equality only if c.d.π = 2 or π ∼= Z. (See Theorem 2.5 of [1].) The L-Betti number condition holds ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7809