1. ## About Subgroups( Algebraic Structures)

1)Define what is meant by the centre / centralizer of C(x) of an element x in a groups G, and prove that C(x) is a subgroup of G

2) Determine which of the elements (16)(24) and (16) lie in the centralizer of (1462) in S6 [ the number 6 is small one not the value ]

Thank you very much

2. Originally Posted by Hyungmin
1)Define what is meant by the centre / centralizer of C(x) of an element x in a groups G, and prove that C(x) is a subgroup of G

2) Determine which of the elements (16)(24) and (16) lie in the centralizer of (1462) in S6 [ the number 6 is small one not the value ]

Thank you very much
I won't define what the centre and centraliser are as they will be in your notes.

To prove that the centraliser of an element is a subgroup you need to show that it is closed under inverses and under multiplication. Where are you stuck with this problem?

To prove that an element is in the centraliser look at your definition of centraliser. Do these two elements commute with $\displaystyle (1462)$?