Show <a> is a subset of C(a) where C(a) is such that xa=ax.

Knowing xa=ax tells me we have an abelian group.

<a> is a cyclic subgroup

we have x=a^n . Need to show x=a^n is a subset of xa=ax. Not sure how to do that

Printable View

- October 21st 2010, 09:05 PMkathrynmathCentralizer proof
Show <a> is a subset of C(a) where C(a) is such that xa=ax.

Knowing xa=ax tells me we have an abelian group.

<a> is a cyclic subgroup

we have x=a^n . Need to show x=a^n is a subset of xa=ax. Not sure how to do that - October 21st 2010, 10:06 PMkathrynmath
I don't know, but this is really frustrating me.

so x=a^n

or x=a*a*a*a*a*a.........

Since <a> is a subgroup, inverses exist

Thus x=a^-1aaaaaaa.....

x=a^n-1

We eventually get x=1

I'm not sure where I'm going wrong in my thought process - October 21st 2010, 10:46 PMtonio