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Mathematics
Linear and Abstract Algebra
Finite vs Ring Groups: Examining Theorems
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[QUOTE="Olinguito, post: 6776447, member: 715504"] [FONT=Times New Roman][SIZE=4]Well, note that $G$ is a group whereas $RG$ is a ring, so not every theorem about $G$ may be applicable to $RG$. For example, $G$ may be a cyclic group, but there is no such thing as a cyclic ring, so a theorem about cyclic groups may not make sense when applied to rings. What you can say is that $RG$ contains a subring isomorphic to $R$, namely $$\{a\cdot e_G:a\in R\}$$ as well as a subset which, with respect to multiplication, forms a group isomorphic to $G$, namely $$\{1_R\cdot g:g\in G\}.$$[/SIZE][/FONT] [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
Finite vs Ring Groups: Examining Theorems
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