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Ricerche di Matematica· 2026Q2

Bounding the order of solvable linear groups with abelian Sylow 2-subgroups

Dingying Ma, Benjamin Lu, Alex Sun, Lina Wang et al.

Short summary

A new bound is established for the order of subgroups within finite solvable groups that possess abelian Sylow 2-subgroups, specifically $|V|^a / \sqrt{6}$ where $a = \frac{3\ln 6}{4\ln 2}$, provided V is a faithful and completely reducible G-module.

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Key points

  • Establishes an upper bound for the order of subgroups in finite solvable groups with abelian Sylow 2-subgroups.
  • The bound is $|V|^a / \sqrt{6}$, with $a = \frac{3\ln 6}{4\ln 2}$, contingent on V being a faithful and completely reducible G-module.
  • A related bound is proven for cases where the order of V is odd.

AI-generated from the title and abstract; the full text is not read.

Abstract

Abstract In this paper, we prove that if H is a subgroup of a finite solvable group G , then H has order at most $$|V|^{a}/\sqrt{6}$$ | V | a / 6 if V is a faithful and completely reducible G -module and H has abelian Sylow 2-subgroups, where $$a=\frac{3\ln 6}{4\ln 2}$$ a = 3 ln 6 4 ln 2 . Furthermore, we establish a similar bound under the additional condition that $$2\not \mid |V|$$ 2 ∤ | V | .

The authors' abstract, as published at the source. Ricerche di Matematica, 2026 · DOI ↗

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Field: Discrete Mathematics and Combinatorics

Discrete Mathematics and CombinatoricsMathematics