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| Articolul urmator |
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| Ultima descărcare din IBN: 2020-09-07 08:01 |
| Căutarea după subiecte similare conform CZU |
| 512.54 (160) |
| Алгебра (400) |
 SM ISO690:2012SKURATOVSKII, Ruslan. Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, nr. 1(92), pp. 3-16. ISSN 1024-7696. |
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 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 1(92) / 2020 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| CZU: 512.54 | ||||||
| MSC 2010: 20B27, 20B22, 20F65, 20B07, 20E45. | ||||||
| Pag. 3-16 | ||||||
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It is proved that the commutator length of an arbitrary element of the iterated wreath product of cyclic groups Cpi , pi ∈ N, is equal to 1. The commutator width of direct limit of wreath product of cyclic groups is found. This paper gives upper bounds of the commutator width (cw(G)) [1] of a wreath product of groups. A presentation in the form of wreath recursion [6] of Sylow 2-subgroups Syl2A2k of A2k is introduced. As a corollary, we obtain a short proof of the result that the commutator width is equal to 1 for Sylow 2-subgroups of the alternating group A2k , where k > 2, permutation group S2k and for Sylow p-subgroups Syl2Apk and Syl2Spk . The commutator width of permutational wreath product B ≀ Cn is investigated. An upper bound of the commutator width of permutational wreath product B ≀Cn for an arbitrary group B is found. |
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| Cuvinte-cheie wreath product of groups, minimal generating set of the commutator subgroup of Sylow 2-subgroups, commutator width of wreath product, commutator width of Sylow p-subgroups, commutator subgroup of alternating group |
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