{'fraction_non_alphanumeric': 0.021739130434782608, 'fraction_numerical': 0.002173913043478261, 'mean_word_length': 5.065789473684211, '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}}
Injectivity and related concepts in modular varieties: I. Two commutator properties

The first property occurred in the investigation of directly representable varieties, and was named C2 by R. McKenzie, the second one is new. Our analysis is independent of injectivity. However, in the forthcoming second part of this paper we are going to prove that varieties with enough injectives satisfy both properties, and shall use intensively the results proved here.