The transitive groups of degree 48 and some applications
نویسندگان
چکیده
The primary purpose of this paper is to report on the successful enumeration in Magma representatives 195826352 conjugacy classes transitive subgroups symmetric group S48 degree 48. In addition, we have determined that 25707 these groups are minimal and 713 them elusive. examples been used enumerate vertex-transitive 48, which there 1538868366, all but 0.1625% arise as Cayley graphs. We also found largest number elements required generate any 10, fact improve previous general bounds third author an arbitrary permutation a given degree. details proof improved bound will be published separate paper.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.06.018