There is a famous lemma saying: "Every subnormal subgroup of a semisimple group is normal and is a semisimple direct factor of the group". Any hints about it? :)
Every subnormal of a semisimple is normal
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group-theory
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0Does $G$ semisimple mean that $G$ is the central product of subgroups $Q_1,..,Q_n \leq G$ such that $[Q_i,Q_i]=Q_i$ and $Q_i/Z(Q_i)$ is simple? – 2015-11-19