AWESOME Trick in INTRO Group Theory!

We prove a special case of Cauchy's famous theorem in group theory: a group G with an even number of elements always has an element of order 2. (An element g of G has order 2 if g ≠ e (the identity element of the group G) and g^2 = e.) The general version of Cauchy's theorem is more difficult but this version can be understood by beginning group theory students with a basic knowledge of the group axioms and consequences of those (in particular, the existence and uniqueness of inverse elements in a group). The video is designed for abstract algebra students at all levels who want to deeply understand how beautiful structural properties of finite groups can be derived from assumptions on their order (number of elements).

Proof of the uniqueness of inverse elements in a group:    • Inverses in a Group are UNIQUE | Intro Gro...  

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