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Minimal embeddings of small finite groups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 9، شماره 3، آذر 2020، صفحه 157-183 اصل مقاله (297.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.112560.1497 | ||
| نویسندگان | ||
| Robert Heffernan1؛ Brendan McCann* 2 | ||
| 1Department of Mathematics, Cork Institute of Technology, Bishopstown, Cork, Ireland. | ||
| 2Department of Computing and Mathematics, Waterford Institute of Technology, Waterford, Ireland | ||
| چکیده | ||
| We determine the groups of minimal order in which all groups of order $n$ can embedded for $ 1 \le n \le 15$. We further determine the minimal order of a group in which all groups of order $n$ or less can be embedded, also for $ 1 \le n \le 15$. | ||
| کلیدواژه‌ها | ||
| Embeddings of groups؛ minimal embeddings؛ small finite groups | ||
| مراجع | ||
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[1] A. Cayley, Desiderata and Suggestions, no. 1, The Theory of Groups, Amer. J. Math., I (1878) 50–52. Reprinted in The Collected Mathematical Papers of Arthur Cayley, Cambridge University Press, x 1898. [2] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985. [3] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.7.2, 2013, http://www.gap-system.org.
[4] R. Heffernan, D. MacHale and B. McCann, Cayley’s Theorem Revisited: Embeddings of Small Finite Groups, Math. Mag., 91-2 (2018) 103–111. [5] I. M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics, 92, American Mathmeatical Society, Providence, Rhode Island, 2008.
[6] B. McCann, On products of cyclic and elementary abelian p-groups, Publ. Math. Debrecen, 91 (2017) 185–216.
[7] R. A. Wilson et al., ATLAS of Finite Group Representations - Version 3, http://brauer.maths.qmul.ac.uk/ Atlas/v3/. [8] R. A. Wilson, The Finite Simple Groups, Springer, London, 2009 | ||
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