Group Theory (C): Find the number of conjugates of (1 2)(3 4) in Sn , n ≥ 4.

Modern Algebra Group Theory (C) Permutation Groups Another Counting Principle Find the number of conjugates of (1 2)(3 4) in Sn , n ≥ 4.

Group Theory (CI): Find the form of all elements commuting with (1 2)(3 4) in Sn , n ≥ 4.

Modern Algebra Group Theory (CI) Permutation Groups Another Counting Principle Find the form of all elements commuting with (1 2)(3 4) in Sn , n ≥ 4.

Group Theory (CII): If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G.

Modern Algebra Group Theory (CII) Permutation Groups Another Counting Principle If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G

Group Theory (CIII): Find two elements in A5 , alternating group of degree 5 , which are conjugate in S5 but not in A5 .

Modern Algebra Group Theory (CIII) Permutation Groups Another Counting Principle Find two elements in A5 , alternating group of degree 5 , which are conjugate in S5 but not in A5 .

Group Theory (CIV): Find all the conjugate classes in A5 and the number of elements in each conjugate class .

Modern Algebra Group Theory (CIV) Permutation Groups Another Counting Principle Find all the conjugate classes in A5 and the number of elements in each conjugate class .