Modern Algebra, Group Theory (XI): In S3 give an example of two elements x,y such that (x.y)^2 ≠ x^2.y^2.

Modern Algebra Group Theory (XI) Symmetric Set of Permutations In S3 give an example of two elements x,y such that (x.y)^2 ≠ x^2.y^2.

Modern Algebra, Group Theory (XII): In S3 show that there are four elements satisfying x^2 = e and three elements satisfying y^3 = e.

Modern Algebra Group Theory (XII) Symmetric Set of Permutations In S3 show that there are four elements satisfying x^2 = e and three elements satisfying y^3 = e.

Modern Algebra, Group Theory (XIII): If G is a finite group, show that there exists a positive integer N such that a^N=e for all aЄG.

Modern Algebra Group Theory (XIII) If G is a finite group, show that there exists a positive integer N such that a^N=e for all aЄG.

Modern Algebra, Group Theory (XIV): Symmetric Set of Permutations:Find order of all elements in S3, where S3 is the symmetric set of permutations of degree 3.

Modern Algebra Group Theory (XIV) Symmetric Set of Permutations Find order of all elements in S3, where S3 is the symmetric set of permutations of degree 3.

Modern Algebra, Group Theory (XV): Abelian Group: If the group G has three elements, show it must be abelian.

Modern Algebra Group Theory (XV) Abelian Group If the group G has three elements, show it must be abelian.