Abstract
Denote the class of finite groups that are the product of two normal supersoluble subgroups and the class of groups that are the product of two subnormal supersoluble subgroups by \(\mathfrak{B}_1\) and \(\mathfrak{B}_2\), respectively. In this paper, a characterisation of groups in \(\mathfrak{B}_1\) or in \(\mathfrak{B}_2\) is given. By applying this new characterisation, some new properties of \(\mathfrak{B}_1\) (\(\mathfrak{B}_2\)) and new proofs of many known results about \(\mathfrak{B}_1\) or \(\mathfrak{B}_2\) are obtained. Further, closure properties of \(\mathfrak{B}_1\) and \(\mathfrak{B}_2\) are discussed.
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We thank the referees for their time and comments.
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The second author has been supported by the project of NSF of China (Grant No. 12071092) and the major project of Basic and Applied Research (Natural Science) in Guangdong Province, China (Grant No. 2017KZDXM058) and the Science and Technology Program of Guangzhou Municipality, China (Grant No. 201804010088)
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Cossey, J., Li, Y.M. On Finite Groups that are the Product of Two Subnormal Supersoluble Subgroups. Acta. Math. Sin.-English Ser. 39, 30–36 (2023). https://doi.org/10.1007/s10114-023-0557-8
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DOI: https://doi.org/10.1007/s10114-023-0557-8