(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a is the only element of order 2 in a group G, prove that a is an element of Z(G).

[Z(G) is the notation used by the book for center of group G]

2. Relevant equations

Z(G)={a is an element of G: ag=ga for every g that is an element of G}

3. The attempt at a solution

I know that if a has order 2 (|a|=2) then a ≠ the identity of the group, say e, and a=a^-1.

I just don't see where I would go from here in showing the center of a group.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Abstract algebra question concerning center of a group

**Physics Forums | Science Articles, Homework Help, Discussion**