Building Blocks of Abelian Groups

Abstract Algebra · Axiom Academy

INTRO Building Blocks of Abelian Groups Discover how every finite abelian group is built from simple cyclic components, like constructing with LEGO blocks! Every finite abelian group can be constructed from cyclic groups - the simplest building blocks in group theory. Let's explore some basic cyclic groups! Click on a cyclic group to see its structure! Select a group above to explore... We can create larger groups by taking the direct product of cyclic groups. Let's build ! The fundamental theorem tells us that every finite abelian group decomposes into prime-power cyclic groups. Let's see how different numbers break down! Explore decompositions for order: Now it's your turn! Select cyclic building blocks to construct an abelian group. Click blocks to add them to your construction. Click blocks above to build your group...

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