Number of sylow subgroups
Is there any inbuilt function in SAGEMATH to compute the number of Sylow subgroups of a permutation group G. If not, can anyone help me to define one such function?
Is there any inbuilt function in SAGEMATH to compute the number of Sylow subgroups of a permutation group G. If not, can anyone help me to define one such function?
Because all Sylow subgroups are conjugate, it is enough to find one and compute its normalizer: the answer will be the index of this normalizer in G
. GAP is the most convenient way to do it which is interfaced in SageMath
sage: G = libgap.DicyclicGroup(12) # a group
sage: p = 2 # a prime
sage: H = libgap.SylowSubgroup(G, p)
sage: N = libgap.Normalizer(G, H)
sage: libgap.Index(G, N)
3
If you have a PermutationGroup
defined from sage, you can use it in place of G
above.
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Asked: 2024-07-10 21:16:48 +0200
Seen: 145 times
Last updated: Jul 10
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