BibTex RIS Kaynak Göster

Identifying long cycles in finite alternating and symmetric groups acting on subsets

Yıl 2015, , 117 - 149, 30.04.2015
https://doi.org/10.13069/jacodesmath.28239

Öz

Let $H$ be a permutation group on a set $\Lambda$, which is permutationally
isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting
on the $k$-element subsets of points from $\{1,\ldots,n\}$, for some
arbitrary but fixed $k$. Suppose moreover that no isomorphism with this
action is known. We show that key elements of $H$ needed to construct such
an isomorphism $\varphi$, such as those whose image under $\varphi$ is an $n$%
-cycle or $(n-1)$-cycle, can be recognised with high probability by the
lengths of just four of their cycles in $\Lambda$.

Kaynakça

  • R. M. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and Á. Seress, A black-box algorithm for recognizing finite symmetric and alternating groups, I, Trans. Amer. Math. Soc., 355, 2097-2113, 2003.
  • S. Bratus and I. Pak, Fast constructive recognition of a black box group isomorphic to Snor Anusing Goldbach’s conjecture, J. Symbolic Comput., 29(1), 33-57, 2000. GAP - Groups, The GAP Group, Algorithms, and Programming, Version 4.7.7, 2015, http://www.gap-system.org.
  • P. Erdős, and P. Turán, On some problems of a statistical group-theory. I, Wahrscheinlichkeitstheorie Verw. Gebiete, 4, 175-186, 1965.
  • P. Erdős, and P. Turán, On some problems of a statistical group-theory. III, Acta Math. Acad. Sci. Hungar., 18 , 309-320, 1967.
  • S. Linton, A. C. Niemeyer and C. E. Praeger, Constructive recognition of Snin its action on k-sets, in preparation. Y. Negi, Recognising large base actions of finite alternating groups, Honours Thesis, School of Math- ematics and Statistifcs, The University of Western Australia, 2006.
  • A. C. Niemeyer and C. E. Praeger, On permutations of order dividing a given integer, J. Algebraic Combinatorics, 26, 125-142, 2007.
  • A. C. Niemeyer and C. E. Praeger, On the proportion of permutations of order a multiple of the degree, J. London Math. Soc., 76, 622-632, 2007.
  • A. C. Niemeyer, C. E. Praeger and Á. Seress, Estimation problems and randomised group algorithms, Probabilistic group theory, combinatorics, and computing, Lecture Notes in Math., 2070, Springer, London, 35-82, 2013.
  • I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, John Wiley & Sons Inc., New York, fifth edition, 1991.
  • Á. Seress, Permutation group algorithms, Cambridge Tracts in Mathematics, 152, Cambridge Uni- versity Press, Cambridge, 2003.
  • R. Warlimont, Über die Anzahl der Lösungen von xn= 1 in der symmetrischen Gruppe Sn, Arch. Math., 30, 591-594, 1978.
Yıl 2015, , 117 - 149, 30.04.2015
https://doi.org/10.13069/jacodesmath.28239

Öz

Kaynakça

  • R. M. Beals, C. R. Leedham-Green, A. C. Niemeyer, C. E. Praeger, and Á. Seress, A black-box algorithm for recognizing finite symmetric and alternating groups, I, Trans. Amer. Math. Soc., 355, 2097-2113, 2003.
  • S. Bratus and I. Pak, Fast constructive recognition of a black box group isomorphic to Snor Anusing Goldbach’s conjecture, J. Symbolic Comput., 29(1), 33-57, 2000. GAP - Groups, The GAP Group, Algorithms, and Programming, Version 4.7.7, 2015, http://www.gap-system.org.
  • P. Erdős, and P. Turán, On some problems of a statistical group-theory. I, Wahrscheinlichkeitstheorie Verw. Gebiete, 4, 175-186, 1965.
  • P. Erdős, and P. Turán, On some problems of a statistical group-theory. III, Acta Math. Acad. Sci. Hungar., 18 , 309-320, 1967.
  • S. Linton, A. C. Niemeyer and C. E. Praeger, Constructive recognition of Snin its action on k-sets, in preparation. Y. Negi, Recognising large base actions of finite alternating groups, Honours Thesis, School of Math- ematics and Statistifcs, The University of Western Australia, 2006.
  • A. C. Niemeyer and C. E. Praeger, On permutations of order dividing a given integer, J. Algebraic Combinatorics, 26, 125-142, 2007.
  • A. C. Niemeyer and C. E. Praeger, On the proportion of permutations of order a multiple of the degree, J. London Math. Soc., 76, 622-632, 2007.
  • A. C. Niemeyer, C. E. Praeger and Á. Seress, Estimation problems and randomised group algorithms, Probabilistic group theory, combinatorics, and computing, Lecture Notes in Math., 2070, Springer, London, 35-82, 2013.
  • I. Niven, H. S. Zuckerman and H. L. Montgomery, An Introduction to the Theory of Numbers, John Wiley & Sons Inc., New York, fifth edition, 1991.
  • Á. Seress, Permutation group algorithms, Cambridge Tracts in Mathematics, 152, Cambridge Uni- versity Press, Cambridge, 2003.
  • R. Warlimont, Über die Anzahl der Lösungen von xn= 1 in der symmetrischen Gruppe Sn, Arch. Math., 30, 591-594, 1978.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Steve Linton Bu kişi benim

Alice C. Niemeyer Bu kişi benim

Cheryl E. Praeger Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2015
Yayımlandığı Sayı Yıl 2015

Kaynak Göster

APA Linton, S., Niemeyer, A. C., & Praeger, C. E. (2015). Identifying long cycles in finite alternating and symmetric groups acting on subsets. Journal of Algebra Combinatorics Discrete Structures and Applications, 2(2), 117-149. https://doi.org/10.13069/jacodesmath.28239
AMA Linton S, Niemeyer AC, Praeger CE. Identifying long cycles in finite alternating and symmetric groups acting on subsets. Journal of Algebra Combinatorics Discrete Structures and Applications. Nisan 2015;2(2):117-149. doi:10.13069/jacodesmath.28239
Chicago Linton, Steve, Alice C. Niemeyer, ve Cheryl E. Praeger. “Identifying Long Cycles in Finite Alternating and Symmetric Groups Acting on Subsets”. Journal of Algebra Combinatorics Discrete Structures and Applications 2, sy. 2 (Nisan 2015): 117-49. https://doi.org/10.13069/jacodesmath.28239.
EndNote Linton S, Niemeyer AC, Praeger CE (01 Nisan 2015) Identifying long cycles in finite alternating and symmetric groups acting on subsets. Journal of Algebra Combinatorics Discrete Structures and Applications 2 2 117–149.
IEEE S. Linton, A. C. Niemeyer, ve C. E. Praeger, “Identifying long cycles in finite alternating and symmetric groups acting on subsets”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 2, ss. 117–149, 2015, doi: 10.13069/jacodesmath.28239.
ISNAD Linton, Steve vd. “Identifying Long Cycles in Finite Alternating and Symmetric Groups Acting on Subsets”. Journal of Algebra Combinatorics Discrete Structures and Applications 2/2 (Nisan 2015), 117-149. https://doi.org/10.13069/jacodesmath.28239.
JAMA Linton S, Niemeyer AC, Praeger CE. Identifying long cycles in finite alternating and symmetric groups acting on subsets. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2:117–149.
MLA Linton, Steve vd. “Identifying Long Cycles in Finite Alternating and Symmetric Groups Acting on Subsets”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 2, sy. 2, 2015, ss. 117-49, doi:10.13069/jacodesmath.28239.
Vancouver Linton S, Niemeyer AC, Praeger CE. Identifying long cycles in finite alternating and symmetric groups acting on subsets. Journal of Algebra Combinatorics Discrete Structures and Applications. 2015;2(2):117-49.