.svg){kind=logo}
ON ORBITS OF WREATH PRODUCT OF FINITE GROUPS
Keywords:
wreath product, group action, finite permutation groups, symmetry groups, application of symmetry groupsDOI:
https://doi.org/10.17654/0972555524002Abstract
We discuss the general relationship between the number of orbits of the wreath product and the orbits of two permutation groups that constitute the wreath product. Examples are provided to illustrate the relationship.
Received: September 19, 2023
Revised: October 3, 2023
Accepted: November 2, 2023
References
M. S. Audu, Wreath product of permutation group, A Research-oriented Course in Arithmetic of Elliptic Curves, Groups and Loops, Lecture Notes Series, National Mathematical Centre, Abuja, 2001.
Dominik Bernhardt et al., Conjugacy classes and centralisers in wreath products, J. Symbolic Comput. 113 (2022), 97-125.
M. Bhattacharijee et al., Notes on Infinite Permutation Groups, Springer, 2006.
B. Davvaz, Groups and Symmetry: Theory and Applications, Springer Nature, 2021.
N. Ghadbane, Wreath product of permutation groups and their actions on a sets, CJMS 10(2) (2021), 142-155.
A. A. Ibrahim and M. S. Audu, On wreath product of permutation groups, Proyecciones 26(1) (2007), 73-90.
L. G. Kovacs, Primitive subgroups of wreath products in product action, Proc. London Math. Soc. 58(3) (1989), 306-322.
W. Liebeck Martin, Cheryl E. Praeger and Jan Saxl, On the O’Nan-Scott theorem for finite primitive permutation groups, J. Austral. Math. Soc. Ser. A 44(3) (1988), 389-396.
J. D. Meldrum, Wreath Products of Groups and Semigroups, CRC Press, 1995.
V. Nekrashevych, Self-similar groups, American Mathematical Society, No. 117, 2005.
O. Ora, Theory of monomial groups, Trans. Amer. Math. Soc. 51 (1942), 15-64. DOI 10.2307/1989979.
C. E. Praeger and Csaba Schneider, Permutation groups and cartesian decompositions, Vol. 449, London Mathematical Society, 2018.
J. S. Rose, A Course on Group Theory, Courier Corporation, 1994.
L. L. Scott, Representations in characteristic p, Santa Cruz Conference on Finite Groups, Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, R.I., Vol. 37, 1980, pp. 318-331.
R. V. Skuratovskii and A. Williams, Irreducible bases and subgroups of a wreath product in applying to diffeomorphism groups acting on the Mobius band, Rend. Circ. Mat. Palermo (2) 70(2) (2021), 721-739.
https://doi.org/10.1007/s12215-020-00514-5.
R. Skuratovskii, Normal subgroups of iterated wreath products of symmetric groups and alternating with symmetric groups, 2021.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
