$\begingroup$ S5's Sylow 2-subgroups actually overlap a lot. The union of the Sylow 2-subgroups of S5 has 1+10+15+30=56 elements, but there are 15 Sylow 2-subgroups of order 8. 15*(8 …

2021年2月7日 · The Sylow Theorems definitely have a lot of non-obvious ideas, and I think expecting someone to come up ...

Now, I know that a Sylow 2 subgroup of S4 has size 8, and that there are either 1 or 3 of them (as the number of of Sylow 2-subgroups has form 1+2k and divides 3, the index). Now my lecturer …

2015年1月20日 · A Sylow 2-subgroup contains at most 3 elements of order 2 because it is of order 4. If there were only 3 such subgroups, there would be at most 9 elements of order 2. …

2014年11月27日 · $\begingroup$ S3 Sylow 2-subgroups: <(12)>, <(13)>, <(23)>. S3 Sylow 3-subgroups: <(123)>. As Quang Hoang and Stadnicki told us, to find the Sylow p-subgroups of …

2019年8月3日 · A student of mine recently showed me this pair of videos (part 1, part 2) by Robert Donley (aka Math Doctor Bob), which attempts to derive the number and structure of …

2015年11月15日 · One may easily prove this theorem by Sylow's third theorem. Indeed, ...

2014年11月12日 · $\begingroup$ If you understand what an irreducible representation is, and how the Sylow subgroups of the symmetric group look like, you can work it out yourself quite …

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2015年3月12日 · If G is the INTERNAL direct product of its Sylow subgroups, then every Sylow subgroup is normal in G. 8 Number of Sylow $7$- and $13$-subgroups in a group of order …