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What is Herstein about?

If a group G has 3, 4, or 5 elements, then G must be abelian (commutative). For groups of order 3, the only possible operation results in an abelian cyclic group of order 3. For groups of order 4, there are two possible operations that both result in abelian groups - a cyclic group of order 4 or the Klein four-group. For groups of order 5, all possible operations lead to abelian groups, shown through examining the possibilities for orders of elements and considering products of distinct elements.

Author

Nadia

Language

EN