The group of words "I also brought a fresh loaf of bread" is not a sentence fragment, which means the statement in the question is false, as seen below.
A sentence fragment can be defined as a group of words that looks like a sentence, but that is missing something essential. A sentence fragment can, for example, be missing the subject or the verb, which means it does not convey a complete message.
That is not the case with "I also brought a fresh loaf of bread." This is a complete sentence. We have the subject "I", the verb "brought" and the object "a fresh loaf of bread." Therefore, we do not have a sentence fragment, but a complete sentence.
We can conclude the statement in the question is false.
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