Perlis-Walker theorem

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

External links

• JSTOR link for Abelian group algebras of finite order by Sam Perlis and Gordon L. Walker