论文标题
具有同构纤维伯恩赛环的组
Groups with isomorphic fibered Burnside rings
论文作者
论文摘要
令$ g $和$ h $为有限组。我们给出了$ g $和$ h $的条件，这意味着$ a $ a $ fibered burnside环$ b^a（g）$和$ b^a（h）$是同构。结果，我们表明存在非同形群体$ g $和$ h $的存在，因此$ b^a（g）$和$ b^a（h）$是同构环。在这里，可以以非平凡的方式选择Abelian Fiber Group $ a $，也就是说，$ b^a（g）$和$ b^a（h）$严格比$ g $和$ h $的伯恩赛德环（Burnside Cond）大，为此，此类反例已知。
Let $G$ and $H$ be finite groups. We give a condition on $G$ and $H$ that implies that the $A$-fibered Burnside rings $B^A(G)$ and $B^A(H)$ are isomorphic. As a consequence, we show the existence of non-isomorphic groups $G$ and $H$ such that $B^A(G)$ and $B^A(H)$ are isomorphic rings. Here, the abelian fiber group $A$ can be chosen in a non-trivial way, that is, such that $B^A(G)$ and $B^A(H)$ are strictly bigger than the Burnside rings of $G$ and $H$, for which such counterexamples are already known.
