Landau's theorem on conjugacy classes for normal subgroups
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Other documents of the author: Beltrán, Antonio; Felipe, Maria José; Melchor Borja, Carmen
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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http://dx.doi.org/10.1142/S0218196716500624 |
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Title
Landau's theorem on conjugacy classes for normal subgroupsDate
2016-10-10Publisher
World ScientificBibliographic citation
BELTRÁN FELIP, Antonio; FELIPE, María José; MELCHOR BORJA, Carmen. Landau's theorem on conjugacy classes for normal subgroups. International Journal of Algebra and Computation (2016), v. 26, n. 7, pp. 1453-1466Type
info:eu-repo/semantics/articlePublisher version
http://www.worldscientific.com/doi/abs/10.1142/S0218196716500624Version
info:eu-repo/semantics/publishedVersionAbstract
Landau’s theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n ... [+]
Landau’s theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n and s, there exist finitely many finite groups G, up to isomorphism, having a normal subgroup N of index n which contains exactly s non-central G-conjugacy classes. Upper bounds for the orders of G and N are obtained; we use these bounds to classify all finite groups with normal subgroups having a small index and few G-classes. We also study the related problems when we consider only the set of G-classes of prime-power order elements contained in a normal subgroup. [-]
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International Journal of Algebra and Computation (2016), v. 26, n. 7Rights
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