ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS
نویسندگان
چکیده
منابع مشابه
On solubility of groups with bounded centralizer chains
The c-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite cdimension k is soluble of derived length bounded in terms of k, and the rank of its quotient by the Hirsch–Plotkin radical is bounded in terms of k. Corollary: a pseudo-(finite soluble) group of finite c-dimension k is soluble of derived length bounde...
متن کاملOn solubility of groups with finitely many centralizers
For any group G, let C(G) denote the set of centralizers of G.We say that a group G has n centralizers (G is a Cn-group) if |C(G)| = n.In this note, we prove that every finite Cn-group with n ≤ 21 is soluble andthis estimate is sharp. Moreover, we prove that every finite Cn-group with|G| < 30n+1519 is non-nilpotent soluble. This result gives a partial answer to aconjecture raised by A. Ashrafi in ...
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Seifert Fibre Groups (SF-Gps) have been introduced and their first derived groups have been worked out in an earlier paper by the author [2,3]. Now we aim to prove that they are residually soluble and residually finite.
متن کاملon solubility of groups with finitely many centralizers
for any group g, let c(g) denote the set of centralizers of g.we say that a group g has n centralizers (g is a cn-group) if |c(g)| = n.in this note, we prove that every finite cn-group with n ≤ 21 is soluble andthis estimate is sharp. moreover, we prove that every finite cn-group with|g| < 30n+1519 is non-nilpotent soluble. this result gives a partial answer to aconjecture raised by a. ashrafi in ...
متن کاملPolynomial Functions on Bounded Chains
We are interested in representations and characterizations of lattice polynomial functions f : L → L, where L is a given bounded distributive lattice. In an earlier paper [4, 5], we investigated certain representations and provided various characterizations of these functions both as solutions of certain functional equations and in terms of necessary and sufficient conditions. In the present pa...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2009
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089508004527