Abstract
Given two positive integers n and c, we determine an upper bound, as a function of n and c, for the maximum order of a finite nilpotent transitive group of degree n and nilpotency class at most c.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. Bosma, J. Cannon, and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), 235–265.
J. D. Dixon, The Fitting subgroup of a linear solvable group, J. Austral. Math. Soc. 7 (1967), 417–424.
P. Lakatoš and V. Ī. Suščans’kiĭ, The coincidence of central series in wreath products I, Publ. Math. Debrecen 23 (1976), 167–176.
P. Pálfy, Estimates for the order of various permutation groups, Contributions to General Algebra 12: Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt 2000, 37–49.
P. Potočnik, P. Spiga, and G. Verret, Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs. arXiv:1010.2546v1 [math.CO].
P. Spiga, Elementary abelian p-groups of rank greater than or equal to 4p−2 are not CI-groups, J. Algebr. Comb. 26 (2007), 343–355.
P. Spiga and G. Verret, On the order of vertex-stabilisers in vertex-transitive graphs with local group \({C_p \times C_p}\) or \({C_p {\rm wr} C_2}\). arXiv:1311.4308 [math.CO].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Crestani, E., Spiga, P. On the maximum order of nilpotent transitive permutation groups. Arch. Math. 103, 313–327 (2014). https://doi.org/10.1007/s00013-014-0689-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-014-0689-2