Abstract
A normal subgroup N of a finite group G is called an n-decomposable subgroup if N is a union of n distinct conjugacy classes of G. Each finite nonabelian nonperfect group is proved to be isomorphic to Q 12, or Z 2 × A 4, or G = 〈a, b, c | a 11 = b 5 = c 2 = 1, b −1 ab = a 4, c −1 ac = a −1, c −1 bc = b −1〉 if every nontrivial normal subgroup is 2- or 4-decomposable.
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Original Russian Text Copyright © 2012 Guo X., Li J., and Shum K. P.
The authors were partially supported by the National Natural Science Foundation of China (Grant 11071155), SRFDP(200802800011), and the Shanghai Leading Academic Discipline Project(J50101).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 3, pp. 558–565, May–June, 2012.
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Guo, X., Li, J. & Shum, K.P. On finite x-decomposable groups for X = {1, 2, 4}. Sib Math J 53, 444–449 (2012). https://doi.org/10.1134/S0037446612020255
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DOI: https://doi.org/10.1134/S0037446612020255