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I am reading Michael Aschbacher's Finite group theory textbook. Exercire 1.6 makes me confused.

1.6 Let H is normal subgroup in G. Then the map L->L/H is a bijection between the set of all subgroups of G containing H and the set of all subgroups of G/H. Normal subgroups correspond to normal subgroups under this bijection.

It is not clear for me what is L. I perused previous paragraphs but didn't find any relevnt information. I will be really thankful if someone would help me to understandhow to solve this exercise.

Arturo Magidin
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zloodeyka
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  • $L$ is such a subgroup of $G$ containing $H$. – Dietrich Burde Apr 22 '20 at 11:00
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    I would not recommend Aschbacher's book for learning elementary group theory. There are gentler books - I would recommend Rotman's book or Dummit and Foote. Aschbacher's book is very demanding and is more suitable for advanced material. – Derek Holt Apr 22 '20 at 11:51

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