Necessary and sufficient conditions for a metacyclic extension to be 2-local and ultrasolvable are established. These conditions are used to prove the ultrasolvability of an arbitrary group extension which has a local ultrasolvable associated subextension of the second type. The obtained reductions enables us to derive ultrasolvability results for a wide class of nonsplit 2-extensions with cyclic kernel.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 460, 2017, pp. 114–133.
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Kiselev, D.D. Metacyclic 2-Extensions with Cyclic Kernel and Ultrasolvability Questions. J Math Sci 240, 447–458 (2019). https://doi.org/10.1007/s10958-019-04362-2
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DOI: https://doi.org/10.1007/s10958-019-04362-2