A sentence, at its minimum, needs to contain both a subject and a verb; further, it must express a complete thought, which enables it to make sense when standing alone.
The above sentence actually expresses two thoughts. First, it states that “A sentence, at its minimum, needs to contain both a subject and a verb.” Second, it states that “it must express a complete thought, which enables it to make sense when standing alone.” Each of those thoughts is also an independent clause. They’re connected by “further,” which is a conjunctive adverb.
Whenever a conjunctive adverb connects two independent clauses, it must be preceded by a semi-colon and followed by a comma.
Other words that can serve as conjunctive adverbs are accordingly, besides, consequently, finally, furthermore, however, nevertheless, and therefore.