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Subgroup proofsno

I would love to have a usual word format answer with detailed proofs.
The problems are 6 in total, the numbers are: from attached page #1: #2.82; 2.86; 2.87, from attached page #2: # 2.97; 2.98; 2.99. Thanks in advance.
The student.


Solution Summary

This is a series of proofs regarding groups and subgroups.