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Group Theory — Between the Lines

From the group axioms to group actions. A six-part series that answers the questions textbooks leave between the lines, building intuition for abstract algebra.

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Folio Official
6 articles
01
Folio Official·February 27, 2026

The group axioms: why these three?

Associativity, identity, inverses -- textbooks present these axioms as if they were carved in stone. But why not two? Why not four? By systematically adding and removing axioms, we discover the engineering brilliance behind the definition of a group.

Group TheoryAlgebraBetween the Lines