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Subgroups of a permutation group

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Garry Buttler

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( 5 months ago )

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.

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Dilpreet Kaur

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( 5 months ago )

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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