Abstract
We provide structural criteria for some finite factorised groups \(G=AB\) when the conjugacy class sizes in G of certain \(\pi \)-elements in \(A\cup B\) are either \(\pi \)-numbers or \(\pi '\)-numbers, for a set of primes \(\pi \). In particular, we extend for products of groups some earlier results.
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M. J. Felipe is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). A. Martínez-Pastor is supported by Proyecto MTM 2014-54707-C3-1-P, Ministerio de Economía, Industria y Competitividad (Spain), and by Proyecto Prometeo/2017/057, Generalitat Valenciana (Spain). The results in this paper are part of the V. M. Ortiz-Sotomayor Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovación y Universidades.
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Felipe, M.J., Martínez-Pastor, A. & Ortiz-Sotomayor, V.M. Products of Groups and Class Sizes of \(\pi \)-Elements. Mediterr. J. Math. 17, 15 (2020). https://doi.org/10.1007/s00009-019-1444-5
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DOI: https://doi.org/10.1007/s00009-019-1444-5