Isomorphic rings of monomial representations
Isomorphic rings of monomial representations
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单项式表示的同构环
DOI：
10.1016/j.jalgebra.2012.06.004
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Michael Müller
中科院分区：
文献类型：
--
作者：
Michael Müller
设D(G)和D（G ~）是奇阶有限群G和G ~的单项式表示的环。证明了D(G) = D（G ~）的同构意味着各Burnside环的同构B(G) = B（G ~）。进一步证明了具有有限z群G和G ~（即只有循环Sylow子群的群）的同构D(G) = D（G ~）隐含了G = G ~的同构。特别地，无平方阶群G是由环D(G)唯一确定直至同构的。
Let D(G) and D(G˜) be the rings of monomial representations of finite groups G and G˜ of odd order. We prove that the isomorphy D(G)≅D(G˜) implies the isomorphy B(G)≅B(G˜) of the respective Burnside rings. Moreover we prove that the isomorphy D(G)≅D(G˜) with finite Z-groups G and G˜ (i.e. groups which have only cyclic Sylow subgroups) implies the isomorphy G≅G˜. In particular a group G of squarefree order is uniquely determined up to isomorphy by the ring D(G).