tlquyen
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 Jul 2 awarded Curious Jan 17 comment Krull dimension of the injective hull of residue field @ Tobias. Thank you! Jan 17 awarded Scholar Jan 17 accepted Linear compact module Jan 17 accepted Existence of a simple submodule Jan 17 accepted If there exists a subgroup contained in all nontrivial subgroups of $G$, then $G$ is quasicyclic. Jan 17 accepted Associate prime ideals and exact sequences of $R$-modules Jan 16 asked Krull dimension of the injective hull of residue field Jan 11 awarded Teacher Jan 11 revised Prove that if $M$ is an $R$-module of finite length, then $\operatorname{End}_R(M)$ is artinian added 1 characters in body Jan 11 awarded Editor Jan 11 revised Prove that if $M$ is an $R$-module of finite length, then $\operatorname{End}_R(M)$ is artinian added 1 characters in body Jan 11 answered Prove that if $M$ is an $R$-module of finite length, then $\operatorname{End}_R(M)$ is artinian Jan 2 comment Subgroup with order $p^s$ contained in a subgroup with oder $p^{s+1}$ Tobias, thank you very much. Jan 2 comment Subgroup with order $p^s$ contained in a subgroup with oder $p^{s+1}$ Oh, this is an exercise in my final test. Can you give me some details about the example that you say about. Thank you! Jan 2 comment Subgroup with order $p^s$ contained in a subgroup with oder $p^{s+1}$ @ Tobias: Ok, a finite $p-$group $G$ has a non-trivial center. But is it true in case G is infinite? Jan 1 comment If there exists a subgroup contained in all nontrivial subgroups of $G$, then $G$ is quasicyclic. Sorry Babak Sorouh for my late. I have learn many thing from your help. Thank you very much! Jan 1 asked Subgroup with order $p^s$ contained in a subgroup with oder $p^{s+1}$ Dec 9 comment If there exists a subgroup contained in all nontrivial subgroups of $G$, then $G$ is quasicyclic. I can see $G$ is torsion and $G\cong G_p$ for some prime $p$. $G$ is dividable if $pG= G$, so suppose $G/pG\ne 0$. I pass to consider $G/pG$ is a $Z_p$-vector space to get something wrong, but I stuck here. Can you give me some help. Dec 6 comment If there exists a subgroup contained in all nontrivial subgroups of $G$, then $G$ is quasicyclic. @ Hagen von Eitzen: Thank. There are some mistakes in my question. The case that I want to mention is : $H\le G$ is a non-trivial subgroup of $G$ and that for every non-trivial subgroup $X\le G$, we have $H\le X$. What do you think about this case?