Class-preserving Coleman automorphisms of finite groups with Wreathed Sylow 2-subgroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910050807709696 |
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| author | Aragona, Riccardo |
| author_facet | Aragona, Riccardo |
| contents | We show that if $G$ is a finite group whose Sylow $2$-subgroups are wreathed, then the intersection $\Outc(G) \cap \OutCol(G)$ has odd order, where $\Outc(G)$ and $\OutCol(G)$ denote the class-preserving and Coleman outer automorphism groups, respectively. This implies that $G$ satisfies the normalizer problem for its integral group ring. Combined with earlier work on the dihedral and semidihedral cases, this settles the question for all three families of $2$-groups of $2$-rank two classified by Gorenstein--Walter and Alperin--Brauer--Gorenstein. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12348 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Class-preserving Coleman automorphisms of finite groups with Wreathed Sylow 2-subgroups Aragona, Riccardo Group Theory Rings and Algebras 20D05, 20D20, 20D45, 16U70 We show that if $G$ is a finite group whose Sylow $2$-subgroups are wreathed, then the intersection $\Outc(G) \cap \OutCol(G)$ has odd order, where $\Outc(G)$ and $\OutCol(G)$ denote the class-preserving and Coleman outer automorphism groups, respectively. This implies that $G$ satisfies the normalizer problem for its integral group ring. Combined with earlier work on the dihedral and semidihedral cases, this settles the question for all three families of $2$-groups of $2$-rank two classified by Gorenstein--Walter and Alperin--Brauer--Gorenstein. |
| title | Class-preserving Coleman automorphisms of finite groups with Wreathed Sylow 2-subgroups |
| topic | Group Theory Rings and Algebras 20D05, 20D20, 20D45, 16U70 |
| url | https://arxiv.org/abs/2603.12348 |