Non-Induced Representations of Finite Cyclic Groups
Non-Induced Representations of Finite Cyclic Groups
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有限循环群的非归纳表示
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Ramanujan Srihari
中科院分区：
文献类型：
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作者：
Ramanujan Srihari
设K是特征为0的代数闭域，G是n阶有限循环群。本文利用关于n的素因子个数的归纳法证明了RK（G）/I ∈ = Z[X]/I ∈ Φn（X）∈其中RK（G）表示G的K-表示的环，I是RK（G）的理想Ind GH（RK（H））的和，当H在G的所有真子群上变化时.这给了我们一个概念，即G的多少表示不是由真子群的表示导出的。
Let K be an algebraically closed field of characteristic 0 and let G be a finite cyclic group of order n. In this note we prove, using induction on the number of prime divisors of n, that RK(G)/I ∼= Z[X]/〈Φn(X)〉 where RK(G) denotes the ring of K-representations of G and I is the sum of ideals Ind G H(RK(H)) of RK(G) as H varies over all proper subgroups of G. This gives us an idea of how many representations of G are not induced from representations of a proper subgroup.