On groups factorized by finitely many subgroups
نویسندگان
چکیده
منابع مشابه
On 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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CONTENTS This article proposes to represent subgroups of finitely presented 1 . Creation of Quotient Representations and Easy Calculations g r o u p s b y t h e i r i m a g e i n a quo t ient. It gives algorithms for basic 2. Subdirect Products operations in this representation and investigates how iteration 3. Iterated Quotient Representations of this approach can be used to extend known quoti...
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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1.1. Baumslag's theorem has another facet. It shows that in the variety 2l of metabelian groups, every finitely generated $I-group G occurs as a subgroup of some finitely presented 2I-group G. The analogous result for the variety of all groups is a celebrated theorem of G. Higman [8] which states that a finitely generated group G is the subgroup of a finitely presented group G if, and only if, ...
متن کاملGroups with countably many subgroups
We describe soluble groups in which the set of all subgroups is countable and show that locally (soluble-byfinite) groups with this property are soluble-by-finite. Further, we construct a nilpotent group with uncountably many subgroups in which the set of all abelian subgroups is countable.
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ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 1999
ISSN: 0041-6053,1573-9376
DOI: 10.1007/bf02592482