Abstract: The following results are proved. Let d be a natural number, and let G be a group of finite even exponent such that each of its finite subgroups is contained in a subgroup isomorphic to the direct product of m dihedral groups, where m ≤ d. Then G is finite (and isomorphic to the direct product of at most d dihedral groups). Next, suppose that G is a periodic group and p is an odd prime. If every finite subgroup of G is contained in a subgroup isomorphic to the direct product D1 × D2, where Di is a dihedral group of order 2pri with natural ri, i = 1,2, then G = M1 × M2, where Mi = Hi,t , ti is an element of order 2, Hi is a locally cyclic p-group, and hti = h−1 for every h ∈ Hi, i = 1,2. Now, suppose that d is a natural number and G is a solvable periodic group such that every of its finite subgroups is contained in a subgroup isomorphic to the direct product of at most d dihedral groups. Then G is locally finite and is an extension of an abelian normal subgroup by an elementary abelian 2-subgroup of order at most 22d.

Cite: Lytkina D.V. , Mazurov V.D.
Periodic groups with one finite nontrivial Sylow 2-subgroup
Proceedings of the Steklov Institute of Mathematics. 2023. V.323, Suppl 1. P.S160-S167. DOI: 10.1134/S0081543823060147 WOS Scopus РИНЦ OpenAlex

Original: Лыткина Д.В. , Мазуров В.Д.
О периодических группах с конечной нетривиальной силовской 2-подгруппой
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2023. Т.29. №4. С.146-154. DOI: 10.21538/0134-4889-2023-29-4-146-154 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	May 5, 2023
Accepted:	Jun 26, 2023
Published print:	Dec 27, 2023
Published online:	Feb 12, 2024

Identifiers:

Web of science:	WOS:001163182700014
Scopus:	2-s2.0-85185302843
Elibrary:	65548169
OpenAlex:	W4391740567

Citing: Пока нет цитирований

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