Could you please explain the meaning of the sentence given below, and whether its grammar is appropriate and/or correct.
Neither were the Jews the only group identified for total destruction because of racial reasons.
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This feels more like a sentence fragment than a complete sentence, since the "neither" explicitly refers back to both previous context and subsequent context to explain the contrast. "Neither" is usually paired with "nor", when listing two (or more) objects, but it's not required. For example:
She likes both red and green, but neither is her favorite color.
Here neither requires previous context to explain. It wouldn't be logical to just say "neither is her favorite color" without saying what her other, non-favorite colors are.
In this same way your example:
"Neither were the Jews ..."
requires previous context to explain what happened with the Jews. It also creates the expectation that the author will explain what other groups were targeted, otherwise the sentence would "leave you hanging".
I took some time to consider whether to study English or History in college. Neither sounded like they would be much fun. So I chose to study Philosophy instead.
To be complete, the sentence in the middle, "Neither sounded like ... " relies on the previous information and (to some extent) the subsequent information. Otherwise it feels like a fragment out of context.
I can of course combine these into one long sentence:
I took some time to consider whether to study English or History in college, but since neither sounded like they would be much fun, I chose to study Philosophy instead.