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Polynomial properties in unitriangular matrices. II
-
Antonio Vera-López
Veröffentlicht/Copyright:
18. November 2005
Abstract
Let 
= (q ) be the
group of all upper unitriangular matrices of size n over 
, the
field with q = pt elements. We show that the
computation of many canonical representatives of the conjugacy classes
of can be reduced to similar calculations for certain matrices of
smaller size that we call condensed matrices. Our methods make use of
combinatorial techniques including (polynomial) generating functions, and they
greatly increase the efficiency of the calculations of the conjugacy vector of
. They also allow us to obtain the number of conjugacy classes of size
q z for any z ≤ 2n − 8. These numbers are
polynomial functions of q, in accordance with a well-known conjecture
of G. Higman.
:
Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Artikel in diesem Heft
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
Artikel in diesem Heft
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
