Prove for a subgroup $N$ of $G$, $$(\forall g \in G): \ gNg^{-1}=N
\implies (\forall g \in G): \ gN=Ng$$ and $$(\forall g \in G): \ gN
\subseteq Ng\implies (\forall g \in G): \ gNg^{-1} \subseteq N$$
Proof 1: Assume $\forall g \in G$ that $gNg^{-1}=N$. Let $n \in N$. Then $\forall g \in ...
I looked through the tag a bit. Michael Hardy identified a further use-case in addition to the two mentioned in the question, namely partitions of intervals in the context of integration, which does not really fall under set partitions.
Further there is something called the partition problem for...
There is still above 1k posts tagged partitions, so a let work to do. Should perhaps information about other tags be added to the tag-excerpt and the tag-wiki?
Suppose $R$ be a Prüfer domain. How should I Prove that it is an arithmetical ring?
Prove for a subgroup $N$ of $G$, $$(\forall g \in G): \ gNg^{-1}=N
\implies (\forall g \in G): \ gN=Ng$$ and $$(\forall g \in G): \ gN
\subseteq Ng\implies (\forall g \in G): \ gNg^{-1} \subseteq N$$
Proof 1: Assume $\forall g \in G$ that $gNg^{-1}=N$. Let $n \in N$. Then $\forall g \in ...
