Mathematics Homework Solutions
#226544
Conjugacy classes
(a) Write out the conjugacy classes explicitly in S_3 and S_4
(b) What are the conjugacy classes in A_4
(c) Since |A_4|=12, any subgroup of order 6 would be normal. Use (b)
to show that A_4 has no subgroup of 6. Conclude that the converse
to LaGrange's theorem is false.
(d) Find a normal subgroup of order 4 in A_4
I need a detailed rigorous proof (solution) to all parts of this problem, so I can study it please.
This provides an example of working with conjugacy classes and subgroups.
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