{'fraction_non_alphanumeric': 0.03259604190919674, 'fraction_numerical': 0.0, 'mean_word_length': 4.584415584415584, '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 Morita equivalence for blocks of finite p-solvable groups in the Glauberman–Isaacs–Watanabe correspondence context

Abstract Let G be a finite p-solvable group for some prime p and let A be a subgroup of Aut(G) with order relatively prime to G, such that A stabilizes a p-block b of G and acts trivially on a defect group P of b. All ordinary characters in b are A-stable by a result of Watanabe. Also there is a block w(b) of CG (A) such that the Glauberman–Isaacs correspondent characters comprise the ordinary irreducible characters of w(b), and there is a Morita equivalence, and hence a perfect isometry, between the blocks b and w(b), given by a bimodule M with vertex ΔP and an endo-permutation module as source and which induces the Glauberman–Isaacs correspondence on the character level. This gives a different proof of results of several authors.