{'fraction_non_alphanumeric': 0.018421052631578946, 'fraction_numerical': 0.002631578947368421, 'mean_word_length': 3.8846153846153846, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A note on group algebras of p-primary abelian groups

Suppose p is a prime number and R is a commutative ring with unity of characteristic 0 in which p is not a unit. Assume that G and H are p-primary abelian groups such that the respective group algebras RG and RH are R-isomorphic. Under certain restrictions on the ideal structure of R, it is shown that G and H are isomorphic.