Although a lot of people think that the pronoun “one” is singular and as such should be followed by a verb in the singular form, it has always been either singular or plural in construction since the beginnings of English. Specifically, when the sense of the statement is “not any persons or things,” the plural usage is more commonly used. This is precisely the sense of the example you presented from that English book, “All the women are fat,
none of them are thin.” We can therefore be confident that the plural usage here, “none of them are thin,” is correct—with practically every major grammar authority backing that usage.
Which is correct? “All the women are fat, none of them are thin”
or “All the women are fat, none of them is thin.”
In contrast, the singular form of the verb is used when “none” is intended to mean “not one” or “not any,” as in the following example: “Of the four leading candidates,
none is a clear winner at this time.” To avoid being needlessly challenged in your usage in such sentences, however, it would be wise to use “not one” instead of “none is”: “Of the four leading candidates,
not one is a clear winner at this time.” It’s absolutely no contest for the singular usage of “none” here.
Of course, it could also be that your idea is that more than one of the candidates are not clear winners. In that case, that sentence could very well use the plural form of “none,” as follows: “Of the four leading candidates,
none are clear winners at this time.” It would be foolhardy for anyone to challenge your plural usage of “none” in this case.
