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 SM ISO690:2012SKURATOVSKII, Ruslan. Minimal generating set and properties of commutator of Sylow subgroups of alternating and symmetric groups. In: Conference on Applied and Industrial Mathematics: CAIM 2018, 20-22 septembrie 2018, Iași, România. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2018, Ediţia a 26-a, pp. 103-106. ISBN 978-9975-76-247-2. |
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| Conference on Applied and Industrial Mathematics Ediţia a 26-a, 2018 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, România, Romania, 20-22 septembrie 2018 | ||||||
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Given a permutational wreath product sequence of cyclic groups [12, 6] of order 2 we research a commutator width of such groups and some properties of its commutator subgroup. Commutator width of Sylow 2-subgroups of alternating group A2k , permutation group S2k and Cp o B were founded. The result of research was extended on subgroups (Syl2A2k )0, p > 2. The paper presents a construction of commutator subgroup of Sylow 2-subgroups of symmetric and alternating groups. Also minimal generic sets of Sylow 2-subgroups of A2k were founded. Elements presentation of (Syl2A2k )0, (Syl2S2k )0 was investigated. We prove that the commutator width [14] of an arbitrary element of a discrete wreath product of cyclic groups Cpi ; pi 2 N is 1. |
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