On odd order nilpotent groups with class 2
نویسندگان
چکیده
منابع مشابه
The Inverse Galois Problem for Nilpotent Groups of Odd Order
Consider any nilpotent group G of finite odd order. We ask if we can always find a galois extension K of Q such that Gal(K/Q) ∼= G. This is the famous Inverse Galois Problem applied to nilpotent groups of finite odd order. By solving the Group Extension Problem and the Embedding Problem, two problems that are related to the Inverse Galois Problem, we show that such a K always exists. A major re...
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We compute the numbers g(n, 2, 2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function P
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Let F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions ζ F2,d(s), prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.
متن کاملMinimal Odd Order Automorphism Groups
We show that 3 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.
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Bailey defined 2-sequencings (terraces) of groups. She conjectured that all finite groups except elementary Abelian 2-groups (other than the cyclic group Z2) have 2-sequencings and proved that the direct product of a 2-sequenceable group and a cyclic group of odd order is 2-sequenceable. It is shown here that all groups of odd order have a special type of 2-sequencing called a starter-translate...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2009
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-009-0071-y