Are there any papers or books that investigate/discuss the relationship between conjugacy classes and normality for the existence of non-trivial homomrphism f:G->H were H is some nontrivial subgroup of G
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1$\begingroup$ Every group has at least one abelian subgroup. Is that what you meant to write? $\endgroup$– Derek HoltCommented Jun 11 at 19:30
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4$\begingroup$ Groups with every subgroup normal are called Dedekind groups, and they have been classified. See here: en.wikipedia.org/wiki/Dedekind_group $\endgroup$– Andy PutmanCommented Jun 11 at 19:32
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$\begingroup$ @AndyPutman In there investigating on Dedekind group they didn't discuss the existence of the homomorphism that I'm looking for. $\endgroup$– NaifCommented Jun 11 at 19:39
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$\begingroup$ @DerekHolt I correct the qustion now $\endgroup$– NaifCommented Jun 11 at 19:45
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$\begingroup$ @Naif: I'm not inclined to do your work for you, but from the classification it should either be trivially true or trivially false. $\endgroup$– Andy PutmanCommented Jun 11 at 19:56
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