{'fraction_non_alphanumeric': 0.017738359201773836, 'fraction_numerical': 0.004434589800443459, 'mean_word_length': 4.136363636363637, '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 Connected Transversals to Nonabelian Subgroups

In this paper we consider groups G which have connected transversals to nonabelian subgroups whose order is a product of two odd primes p and q, where pq andp= 2 qm+ 1. In our main theorem we show thatG is then solvable. We apply our results to loop theory and it follows that if the inner mapping group of a finite loop has order pq, where p and q are as previously given, then the loop is solvable.