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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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The permutation group S4S4 is defined as the group of all possible permutations of [1234].
i) Find the number of subgroups of S4S4 that have order 2.
ii) A: { [1234], [2143], [3412], [4321] } and B: { [1234], [1243], [2134], [2143] }. Which of A and B are subgroups of S4S4?
Trying to teach myself a Further Maths module on Groups is proving difficult when none of my teachers know the syllabus, any help would be appreciated! Thanks.
i) You want all transpositions (ab), and all pairs of disjoint transpositions (ab)(cd).
ii) Assuming that [2143] means, in cycle notation, (12)(34), then A is a subgroup.
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