School of Mathematics & Physics, University of Lincoln
Despite current difficulties in international travel, new online collaboration of Evgeny Khukhro (Univ. of Lincoln) with algebraists in Spain (Alexander Moretó, Univ. of Valencia) and Iran (Mohammad Zarrin, Univ. of Kurdistan) produced new results about finite groups, which give an answer to a question of Andrei Jaikin-Zapirain. These results have now been submitted as a paper “The average element order and the number of conjugacy classes of finite groups”. Apart from the relevant counterexamples constructed using the so-called secretive p-groups, the paper explores links with other parts of group theory such as number of conjugacy classes, anti-Hughes groups, connections with identities of the associated Lie ring of a free group of prime exponent, etc.