Perlis-Walker theorem

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This fact is related to: group rings
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Statement

Let G and H be finite Abelian groups. Then, the group algebra \mathbb{Q}(G) is isomorphic to the group algebra \mathbb{Q}(H) if and only if G is isomorphic to H.

This is a step in the direction of solving the isomorphic group algebra problem, which asks for conditions under which algebra-isomorphic groups are isomorphic.

References

  • Abelian group algebras of finite order by Sam Perlis and Gordon L. Walker, Transactions of the American Mathematical Society, Vol. 68, No. 3. (May, 1950), pp. 420-426

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