Prove that if a is the only element of order 2 in a group, then a lies in the center of the grou

Name: Prove that if a is the only element of order 2 in a group, then a lies in the center of the group.
Uploaded: 2023-10-19T19:15:06-08:00
Duration: 3 min 38 s
Channel: Mengchun Cai
Description: Prove that if a is the only element of order 2 in a group, then a lies in the center of the group.

Question

Zhumagali Shomanov · Accepted Answer

1. We are given that $a$ is the only element of order 2 in the group. This means that $a^2 = e$,

Question

Prove that if $a$ is the only element of order 2 in a group, then $a$ lies in the center of the group.

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