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Connected components of the category of elementary abelian $p$-subgroups.

Research output: Contribution to Journal/Magazine › Journal article

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Connected components of the category of elementary abelian $p$-subgroups. / Mazza, Nadia.
In: Journal of Algebra, Vol. 320, No. 12, 15.12.2008, p. 4242-4248.

Research output: Contribution to Journal/Magazine › Journal article

Harvard

Mazza, N 2008, 'Connected components of the category of elementary abelian $p$-subgroups.', Journal of Algebra, vol. 320, no. 12, pp. 4242-4248. https://doi.org/10.1016/j.jalgebra.2008.07.028

APA

Mazza, N. (2008). Connected components of the category of elementary abelian $p$-subgroups. Journal of Algebra, 320(12), 4242-4248. https://doi.org/10.1016/j.jalgebra.2008.07.028

Vancouver

Mazza N. Connected components of the category of elementary abelian $p$-subgroups. Journal of Algebra. 2008 Dec 15;320(12):4242-4248. doi: 10.1016/j.jalgebra.2008.07.028

Author

Mazza, Nadia. / Connected components of the category of elementary abelian $p$-subgroups. In: Journal of Algebra. 2008 ; Vol. 320, No. 12. pp. 4242-4248.

Bibtex

@article{757acff5326d4bc48e0c2e64e4fbfeb8,
title = "Connected components of the category of elementary abelian $p$-subgroups.",
abstract = "We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime $p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is $p+1$ if $G$ has rank $2$. More precisely, if $G$ has rank $2$, there are exactly $1,~2,~p+1$, or possibly $3$ classes for some $3$-groups of maximal nilpotency class.",
keywords = "p-groups, Elementary abelian p-subgroups, Posets of p-subgroups, Group of endotrivial modules",
author = "Nadia Mazza",
note = "The final, definitive version of this article has been published in the Journal, Journal of Algebra 320 (12), 2008, {\textcopyright} ELSEVIER.",
year = "2008",
month = dec,
day = "15",
doi = "10.1016/j.jalgebra.2008.07.028",
language = "English",
volume = "320",
pages = "4242--4248",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "ELSEVIER ACADEMIC PRESS INC",
number = "12",

}

RIS

TY - JOUR

T1 - Connected components of the category of elementary abelian $p$-subgroups.

AU - Mazza, Nadia

N1 - The final, definitive version of this article has been published in the Journal, Journal of Algebra 320 (12), 2008, © ELSEVIER.

PY - 2008/12/15

Y1 - 2008/12/15

N2 - We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime $p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is $p+1$ if $G$ has rank $2$. More precisely, if $G$ has rank $2$, there are exactly $1,~2,~p+1$, or possibly $3$ classes for some $3$-groups of maximal nilpotency class.

AB - We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime $p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is $p+1$ if $G$ has rank $2$. More precisely, if $G$ has rank $2$, there are exactly $1,~2,~p+1$, or possibly $3$ classes for some $3$-groups of maximal nilpotency class.

KW - p-groups

KW - Elementary abelian p-subgroups

KW - Posets of p-subgroups

KW - Group of endotrivial modules

U2 - 10.1016/j.jalgebra.2008.07.028

DO - 10.1016/j.jalgebra.2008.07.028

M3 - Journal article

VL - 320

SP - 4242

EP - 4248

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 12

ER -