Cosets of normal subgroups and powers of conjugacy classes
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Title
Cosets of normal subgroups and powers of conjugacy classesDate
2021-08-03Publisher
WileyISSN
0025-584X; 1522-2616Bibliographic citation
Beltrán, A, Felipe, MJ. Cosets of normal subgroups and powers of conjugacy classes. Mathematische Nachrichten. 2021; 1– 5. https://doi.org/10.1002/mana.201900554Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/acceptedVersionAbstract
Let 𝐺 be a finite group and let𝐾 = 𝑥𝐺 be the conjugacy class of an element 𝑥 of 𝐺. In this paper, it is proved that if 𝑁 is a normal subgroup of 𝐺 such that the coset 𝑥𝑁 is the union of 𝐾 and 𝐾−1 (the ... [+]
Let 𝐺 be a finite group and let𝐾 = 𝑥𝐺 be the conjugacy class of an element 𝑥 of 𝐺. In this paper, it is proved that if 𝑁 is a normal subgroup of 𝐺 such that the coset 𝑥𝑁 is the union of 𝐾 and 𝐾−1 (the conjugacy class of the inverse of 𝑥), then 𝑁 and the subgroup ⟨𝐾⟩ are solvable. As an application, we prove that if there exists a natural number 𝑛 ≥ 2 such that 𝐾𝑛 = 𝐾 ∪𝐾−1, then ⟨𝐾⟩ is solvable. [-]
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Mathematische Nachrichten, 2021Funder Name
Spanish Government | Universitat Jaume I
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PGC2018-096872-B-I00 | UJI-B2019-03
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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