scholarly journals Fixed point free automorphisms of groups related to finite fields

2012 ◽  
Vol 18 (4) ◽  
pp. 661-673
Author(s):  
Lindsay N. Childs
Keyword(s):  
Fixed Point ◽  
Finite Fields ◽  
Automorphisms Of Groups

scholarly journals Derangements in cosets of primitive permutation groups

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Andrei Pavelescu
Keyword(s):  
Fixed Point ◽  
Finite Fields ◽  
Permutation Groups ◽  
Normal Subgroups ◽  
Primitive Groups ◽  
Branched Coverings ◽  
Affine Groups ◽  
Nonabelian Subgroup ◽  
Projective Curves ◽  
Curves Over Finite Fields

AbstractMotivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups. Using the Aschbacher–O'Nan–Scott Theorem for primitive groups to partition the problem, we provide complete answers for affine groups and groups which contain a regular normal nonabelian subgroup.

scholarly journals Involutory Automorphisms of Groups of odd Order and Their Fixed Point Groups

1966 ◽  
Vol 27 (1) ◽  
pp. 113-120 ◽  
Author(s):  
L. G. Kovács ◽  
G. E. Wall
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Odd Order ◽  
Point Groups ◽  
A Finite Group ◽  
Automorphisms Of Groups ◽  
Elementary Result

Let G be a finite group of odd order with an automorphism θ of order 2. (We use without further reference the fact, established by W. Feit and J. G. Thompson, that all groups of odd order are soluble.) Let Gθ denote the subgroup of G formed by the elements fixed under θ. It is an elementary result that if Gθ = 1 then G is abelian. But if we merely postulate that Gθ be cyclic, the structure of G may be considerably more complicated—indeed G may have arbitrarily large soluble length.

scholarly journals On Additive invariants of actions of additive and multiplicative groups

2013 ◽  
Vol 12 (3) ◽  
pp. 551-568 ◽  
Author(s):  
Wenchuan Hu
Keyword(s):  
Fixed Point ◽  
Algebraic Group ◽  
Finite Fields ◽  
Algebraic Variety ◽  
Characteristic Zero ◽  
Multiplicative Group ◽  
Fixed Point Set ◽  
Projective Varieties ◽  
Point Set ◽  
Multiplicative Groups

AbstractLet X be an algebraic variety with an action of either the additive or multiplicative group. We calculate the additive invariants of X in terms of the additive invariants of the fixed point set, using a formula of Białynicki-Birula. The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain results on the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields. As applications, we obtain the l-adic Euler-Poincaré characteristic for the Chow varieties of certain projective varieties over a field of arbitrary characteristic. Moreover, we show that the virtual Hodge (p,0) and (0,q)-numbers of the Chow varieties and affine algebraic group varieties are zero for all p,q positive.

scholarly journals Bruhat Order on Partial Fixed Point Free Involutions

10.37236/4396 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Mahir Bilen Can ◽  
Yonah Cherniavsky ◽  
Tim Twelbeck
Keyword(s):  
Fixed Point ◽  
Zeta Function ◽  
Finite Fields ◽  
Generating Function ◽  
Bruhat Order ◽  
Symmetric Matrices ◽  
Order Complex ◽  
Orbit Closures

The order complex of inclusion poset $PF_n$ of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that $PF_n$ is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of $PF_n$ is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields
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