On the influence of the fixed points of an automorphism to the structure of a group
| buir.contributor.author | Kızmaz, Muhammet Yasir | |
| buir.contributor.orcid | Kızmaz, Muhammet Yasir|0000-0002-8277-4469 | |
| dc.citation.epage | 336 | en_US |
| dc.citation.spage | 326 | en_US |
| dc.citation.volumeNumber | 572 | en_US |
| dc.contributor.author | Kızmaz, Muhammet Yasir | |
| dc.date.accessioned | 2022-03-02T12:51:54Z | |
| dc.date.available | 2022-03-02T12:51:54Z | |
| dc.date.issued | 2021-01-06 | |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | Let α be a coprime automorphism of a group G of prime order and let P be an α-invariant Sylow p-subgroup of G. Assume that p∉π(CG(α)). Firstly, we prove that G is p-nilpotent if and only if CNG(P)(α) centralizes P. In the case that G is Sz(2r) and PSL(2,2r)-free where r=|α|, we show that G is p-closed if and only if CG(α) normalizes P. As a consequence of these two results, we obtain that G≅P×H for a group H if and only if CG(α) centralizes P. We also prove a generalization of the Frobenius p-nilpotency theorem for groups admitting a group of automorphisms of coprime order. | en_US |
| dc.description.provenance | Submitted by Dilan Ayverdi (dilan.ayverdi@bilkent.edu.tr) on 2022-03-02T12:51:54Z No. of bitstreams: 1 On_the_influence_of_the_fixed_points_of_an_automorphism_to_the_structure_of_a_group.pdf: 331142 bytes, checksum: 881b2685f9dfce76954bab01636ea54c (MD5) | en |
| dc.description.provenance | Made available in DSpace on 2022-03-02T12:51:54Z (GMT). No. of bitstreams: 1 On_the_influence_of_the_fixed_points_of_an_automorphism_to_the_structure_of_a_group.pdf: 331142 bytes, checksum: 881b2685f9dfce76954bab01636ea54c (MD5) Previous issue date: 2021-01-06 | en |
| dc.identifier.doi | 10.1016/j.jalgebra.2020.12.025 | en_US |
| dc.identifier.eissn | 1090-266X | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/11693/77664 | |
| dc.language.iso | English | en_US |
| dc.publisher | Academic Press | en_US |
| dc.relation.isversionof | https://doi.org/10.1016/j.jalgebra.2020.12.025 | en_US |
| dc.source.title | Journal of Algebra | en_US |
| dc.subject | P-closed | en_US |
| dc.subject | P-nilpotency | en_US |
| dc.subject | Coprime action | en_US |
| dc.title | On the influence of the fixed points of an automorphism to the structure of a group | en_US |
| dc.type | Article | en_US |
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