A simple group of order 44,352,000

• Published in 1968
• Added on 2024-04-02

The group \(G\) of the title is obtained as a primitive permutation group of degree 100 in which the stabilizer of a point has orbits of lengths 1, 22 and 77 and is isomorphic to the Mathieu group \(M_{22}\). Thus \(G\) has rank 3 in the sense of [1]. \(G\) is an automorphism group of a graph constructed from the Steiner system \(\mathfrak{S}(3, 6, 22)\).

Links

• https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46258/209_2005_Article_BF01110435.pdf
• https://link.springer.com/article/10.1007/BF01110435
• https://link.springer.com/content/pdf/10.1007/BF01110435.pdf

Other information

BibTeX entry

@article{Asimplegroupoforder44352000,
	key = {Asimplegroupoforder44352000},
	type = {article},
	title = {A simple group of order 44,352,000},
	author = {Higman, Donald G. and Sims, Charles C.},
	abstract = {The group \(G\) of the title is obtained as a primitive permutation group of degree 100 in which the stabilizer of a point has orbits of lengths 1, 22 and 77 and is isomorphic to the Mathieu group \(M{\_}{\{}22{\}}\). Thus \(G\) has rank 3 in the sense
of [1]. \(G\) is an automorphism group of a graph constructed from the Steiner system \(\mathfrak{\{}S{\}}(3, 6, 22)\).},
	comment = {},
	date_added = {2024-04-02},
	date_published = {1968-12-07},
	urls = {https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46258/209{\_}2005{\_}Article{\_}BF01110435.pdf,https://link.springer.com/article/10.1007/BF01110435,https://link.springer.com/content/pdf/10.1007/BF01110435.pdf},
	collections = {the-groups-group},
	url = {https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46258/209{\_}2005{\_}Article{\_}BF01110435.pdf https://link.springer.com/article/10.1007/BF01110435 https://link.springer.com/content/pdf/10.1007/BF01110435.pdf},
	urldate = {2024-04-02},
	year = 1968,
	publisher = {Springer-Verlag},
	fulltext_html_url = {https://link.springer.com/article/10.1007/BF01110435},
	journal = {Mathematische Zeitschrift},
	issn = {1432-1823},
	volume = 105,
	issue = 2,
	identifier = {doi:10.1007/BF01110435},
	doi = {10.1007/BF01110435},
	pages = {110-113}
}