{'fraction_non_alphanumeric': 0.024054982817869417, 'fraction_numerical': 0.003436426116838488, 'mean_word_length': 5.010309278350515, '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}}
On the classification of prime‐power groups by coclass

By giving a constructive proof of Conjecture P of Newman and O’Brien, we reduce the classification of certain p‐groups of coclass r to a finite calculation. For the case p=2 we show that all 2‐groups of coclass r can be classified by finitely many parametrised presentations. A non‐constructive proof of Conjecture P was given by du Sautoy, using the theory of zeta functions. Our constructive proof uses homological algebra. It yields more precise results and detailed structure theorems for the p‐groups under consideration.