Abstract
Given a class ℑ of finite groups, a subgroup H of a group G is called ℑ n -normal in G if there exists a normal subgroup T of G such that HT is a normal subgroup of G and (H ∩ T)H G /H G is contained in the ℑ-hypercenter Z ℑ∞ (G/H G ) of G/H G . We obtain some results about the ℑ n -normal subgroups and use them to study the structure of some groups.
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Original Russian Text Copyright © 2011 Guo W. and Yu X.
The authors were supported by a NNSF of China (Grant 11071229). Hefei; Xuzhou.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 2, pp. 250–264, March–April, 2011.
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Guo, W., Yu, X. On ℑ n -normal subgroups of finite groups. Sib Math J 52, 197–206 (2011). https://doi.org/10.1134/S0037446611020029
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DOI: https://doi.org/10.1134/S0037446611020029