maximal independent sets and maximal independent generating sets of PSL(2,p)

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I'm searching for an example of a group PSL(2,p) with a "maximal independent" set of length greater than the length of a "maximal independent generating" set. All authors refer to Whiston's papers "Maximal Independent Generating Sets of the Symmetric Group" and "On the maximal size of independent generating sets", but I didn't find an example in these articles.