Fusion systems containing pearls

Valentina Grazian

doi:10.1016/j.jalgebra.2018.05.029

Fusion systems containing pearls

Valentina Grazian

Mathematical Science

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

4 Downloads (Pure)

Abstract

An f-essential subgroup is called a pearl if it is either elementary abelian of order p² or non-abelian of order p³. In this paper we start the investigation of fusion systems containing pearls: we determine a bound for the order of p-groups containing pearls and we classify the saturated fusion systems on p-groups containing pearls and having sectional rank at most 4.

Original language	English
Pages (from-to)	98-140
Number of pages	43
Journal	Journal of Algebra
Volume	510
Early online date	15 Jun 2018
DOIs	https://doi.org/10.1016/j.jalgebra.2018.05.029
Publication status	Published - 15 Sept 2018

Bibliographical note

The main theorems of this paper are generalizations of results proved by the author in her PhD thesis, under the supervision of Prof. Chris Parker. She is immensely grateful to him for his support. She would also like to show her gratitude to Dr. Ellen Henke for comments that improved this manuscript.

Keywords

Fusion systems
Pearls
Qd(p)
groups
Elementary abelian essential subgroup
Extraspecial essential subgroup
p-Groups of maximal nilpotency class
--Groups of sectional rank at most 4

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10.1016/j.jalgebra.2018.05.029Licence: Unspecified

Accepted Manuscript
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 539 KBLicence: CC BY-NC-ND

Cite this

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author = "Valentina Grazian",

note = "The main theorems of this paper are generalizations of results proved by the author in her PhD thesis, under the supervision of Prof. Chris Parker. She is immensely grateful to him for his support. She would also like to show her gratitude to Dr. Ellen Henke for comments that improved this manuscript.",

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N2 - An f-essential subgroup is called a pearl if it is either elementary abelian of order p2 or non-abelian of order p3. In this paper we start the investigation of fusion systems containing pearls: we determine a bound for the order of p-groups containing pearls and we classify the saturated fusion systems on p-groups containing pearls and having sectional rank at most 4.

AB - An f-essential subgroup is called a pearl if it is either elementary abelian of order p2 or non-abelian of order p3. In this paper we start the investigation of fusion systems containing pearls: we determine a bound for the order of p-groups containing pearls and we classify the saturated fusion systems on p-groups containing pearls and having sectional rank at most 4.

KW - Fusion systems

KW - Pearls

KW - Qd(p)

KW - groups

KW - Elementary abelian essential subgroup

KW - Extraspecial essential subgroup

KW - p-Groups of maximal nilpotency class

KW - --Groups of sectional rank at most 4

U2 - 10.1016/j.jalgebra.2018.05.029

DO - 10.1016/j.jalgebra.2018.05.029

M3 - Article

SN - 0021-8693

VL - 510

SP - 98

EP - 140

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Fusion systems containing pearls

Abstract

Bibliographical note

Keywords

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