We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
COMMUTATOR WIDTH IN THE WREATH PRODUCT, COMMUTATOR SUBGROUP OF SYLOW 2-SUBGROUPS OF ALTERNATING GROUP AND SYMMETRIC GROUPS.
- Authors
Skuratovskii, Ruslan
- Abstract
The size of a minimal generating set for the commutator subgroup of Sylow 2-subgroups of alternating group is found. The structure of commutator subgroup of Sylow 2-subgroups of the alternating group A2k is investigated. It is shown that (Syl2A2k)2 = Syl'2A2k, k > 2. It is proved that the commutator length of an arbitrary element of the iterated wreath product of cyclic groups CPi, Pi € N equals to 1. The commutator width of direct limit of wreath product of cyclic groups is found. This paper presents upper bounds of the commutator width (cw(G)) [1] of a wreath product ofgroups. A recursive presentation of Sylows 2-subgroups Syl2(A2k) of A2k is introduced. As a result the short proof that the commutator width of Sylow 2-subgroups of alternating group A2k, permutation group S2k and Sylow p-subgroups of Syl2Apk (Syl2Spk) are equal to 1 is obtained. A 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.
- Subjects
SYLOW subgroups; COMMUTATION (Electricity); PERMUTATION groups; CYCLIC groups; COMMUTATORS (Operator theory); GROUP products (Mathematics); WREATH products (Group theory)
- Publication
ROMAI Journal, 2019, Vol 15, Issue 1, p117
- ISSN
1841-5512
- Publication type
Article