If the child has been a permanent resident for at least 5 years, then she is eligible to apply for naturalization
on her own. It does not require the mother to become a US citizen, if the mother is not yet eligible to do so.
You can look at the green card itself, to determine how long the child has been a permanent resident. Then add 5 years from that date to determine when she is eligible to naturalize.
NOTE: The application (N-400
) itself can be filed 90 days prior to completion of the 5th year, to start the processing. So at 4 years, 275 days, the naturalization application can be submitted.
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