Use groupby.transform ?

This does the job. This works on large datasets.

import pandas as pd

df = pd.DataFrame({
    "group": ["A", "A", "B", "B", "B", "C"],
    "value": [10, 14, 3, 4, 9, 20],
})
df["value_centered"] = df["value"] - df.groupby("group")["value"].transform("mean")

print(df)