Guralnick, Robert and Wang, Daqing, \Bounds for Fixed Point Free Elements in a Transitive Group and Applications to Curves over Finite Fields, Israel J. Math. 101 (1997), 255-287. Home/Search Document Details and Download
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Computational Arithmetic Geometry I: Sentences Nearly In The.. - Rojas (2000) (Correct)
....least one xed point. Then j G 1 1 N . The proof occupies the second page of [CC92] and requires only some basic group representation theory. 9 The upper bound is tight, but completely classifying the next lower values of j G currently requires the classi cation of nite simple groups [GW97]. The latter classi cation will not be necessary for our results. Proof of Assertion (1) First note that by assumption, V F #Z F 2. Furthermore, by theorems 5 and 10, j F 1 1 VF . So by theorem 9 we are done. Remark 11. From our proofs above we easily see that the asymptotic bound from ....
Guralnick, Robert and Wang, Daqing, \Bounds for Fixed Point Free Elements in a Transitive Group and Applications to Curves over Finite Fields, Israel J. Math. 101 (1997), 255-287.
Permutations - Cameron (Correct)
....to Frobenius. It can be quantified in various ways. For example, Cameron and Cohen [22] showed that at least a fraction 1=n of the elements of G are derangements, and determined all groups meeting the bound; they gave stronger bounds under additional hypotheses, as also did Guralnick and Wang [55]. Problem 4. For which classes of transitive permutation groups is the proportion of derangements bounded away from zero Fein, Kantor and Schacher [43] extended this in a different direction. They showed: Theorem 2.3 Every finite transitive permutation group of degree greater than 1 contains a ....
R. Guralnick and D. Wan, Bounds for fixed point free elements in a transitive group and applications to curves over finite fields, Israel J. Math. 101 (1997), 255--287.
The rational function analogue of a question of Schur and .. - Guralnick, Müller, Saxl (1999) Self-citation (Guralnick) (Correct)
....i=1 [CG (g i ) CH (g i ) 17 where g 1 ; g m is a set of representatives for the H conjugacy classes of g G H. Proof. g) jCG (g)jjg G H j=jH j = jCG (g)j X jg H i j=jH j = X [CG (g i ) CH (g i ) The next two results are essentially in [FGS93, 13.1] See also [GW97, Section 3] Lemma 3.9. Let A be a finite group with G a normal subgroup with A=G cyclic generated by xG. Suppose A acts on a finite set Omega . Then P g2G (xg) rjGj, where r is the number of common orbits that A and G have on Omega . In particular, if A and G are both transitive on ....
R. Guralnick, D. Wan, Bounds for fixed point free elements in a transitive group and applications to curves over finite fields, Israel J. Math. (1997), 101, 255--287.
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