2018-11-21T07:39:16Zhttp://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1666472018-11-08T08:52:31Zcom_10234_7037com_10234_9col_10234_8635
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Beltrán Felip, Antonio
author
Felipe, María José
author
Melchor Borja, Carmen
author
2016-10-10
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.
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. 1453-1466
http://hdl.handle.net/10234/166647
http://dx.doi.org/10.1142/S0218196716500624
Finite groups
Conjugacy classes
Normal subgroups
Number of conjugacy classes
Landau's theorem on conjugacy classes for normal subgroups