منابع مشابه
NILPOTENT p-LOCAL FINITE GROUPS
In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
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Let G be a nite group and let i (G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the i 's are established. In particular it is shown that i = k i jGj=jGj 2 for some non-negative integers k i and that P 1 i=1 i is either 1 or at most 1/2 for solvable groups.
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In this paper we investigate the structure of groups as in the title. Our work builds on work of several other authors, namely Konyuh [5], Leedham-Green and Plesken [6], and Zalesskii [10], who have described the abstract isomorphism types of the groups. We obtain more detailed descriptions, in particular explaining how group structure depends on the existence of an abelian primitive subgroup. ...
متن کاملIrredundant Generating Sets of Finite Nilpotent Groups
It is a standard fact of linear algebra that all bases of a vector space have the same cardinality, namely the dimension of the vector space over its base field. If we treat a vector space as an additive abelian group, then this is equivalent to saying that an irredundant generating set for a vector space must have cardinality equal to the dimension of the vector space. The same is not true for...
متن کاملNilpotent Groups of Finite Morley Rank
Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.2307/2035864