Step 1: Recall the family of blotting techniques.
Molecular biology uses different blotting names depending on which molecule is being transferred and detected, DNA, RNA, or protein.
Step 2: Match the molecule in the question.
The question specifically talks about DNA fragments moving from an agarose gel onto a nylon membrane.
Step 3: Name the technique.
This DNA specific transfer method was developed by Edwin Southern and is called Southern blotting, RNA transfer would instead be called Northern blotting and protein transfer Western blotting.
Final answer: Option 1, Southern blotting.