Finite loops arising from projective 3-space

Silvia Pianta; Stefano Pasotti; Elena Zizioli

doi:10.1007/s13366-017-0356-4

Finite loops arising from projective 3-space

Silvia Pianta, Stefano Pasotti, Elena Zizioli

Università Cattolica del Sacro Cuore

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

By means of the method of transversals and sections we build up (left) loops (L, ∗) contained in the group G where G = PGL_2 (q) or G = PSL 2_(q), q > 3 odd. Since such groups can be embedded in PG(3, q), the subgroups we considered for the construction of (L, ∗) are geometrically relevant (lines or planes of PG(3, q)) or algebraically relevant (maximal subgroups).

Lingua originale	English
pagine (da-a)	155-165
Numero di pagine	11
Rivista	Beitrage zur Algebra und Geometrie
Volume	59
DOI	https://doi.org/10.1007/s13366-017-0356-4
Stato di pubblicazione	Pubblicato - 2018

Keywords

Left loop, loop transversal, PGL_2(q), PSL_2(q)

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10.1007/s13366-017-0356-4

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abstract = "By means of the method of transversals and sections we build up (left) loops (L, ∗) contained in the group G where G = PGL_2 (q) or G = PSL 2_(q), q > 3 odd. Since such groups can be embedded in PG(3, q), the subgroups we considered for the construction of (L, ∗) are geometrically relevant (lines or planes of PG(3, q)) or algebraically relevant (maximal subgroups).",

keywords = "Left loop, loop transversal, PGL_2(q), PSL_2(q), Left loop, loop transversal, PGL_2(q), PSL_2(q)",

author = "Silvia Pianta and Stefano Pasotti and Elena Zizioli",

year = "2018",

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language = "English",

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T1 - Finite loops arising from projective 3-space

AU - Pianta, Silvia

AU - Pasotti, Stefano

AU - Zizioli, Elena

PY - 2018

Y1 - 2018

N2 - By means of the method of transversals and sections we build up (left) loops (L, ∗) contained in the group G where G = PGL_2 (q) or G = PSL 2_(q), q > 3 odd. Since such groups can be embedded in PG(3, q), the subgroups we considered for the construction of (L, ∗) are geometrically relevant (lines or planes of PG(3, q)) or algebraically relevant (maximal subgroups).

AB - By means of the method of transversals and sections we build up (left) loops (L, ∗) contained in the group G where G = PGL_2 (q) or G = PSL 2_(q), q > 3 odd. Since such groups can be embedded in PG(3, q), the subgroups we considered for the construction of (L, ∗) are geometrically relevant (lines or planes of PG(3, q)) or algebraically relevant (maximal subgroups).

KW - Left loop, loop transversal, PGL_2(q), PSL_2(q)

UR - http://hdl.handle.net/10807/115281

U2 - 10.1007/s13366-017-0356-4

DO - 10.1007/s13366-017-0356-4

M3 - Article

VL - 59

SP - 155

EP - 165

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

ER -

Finite loops arising from projective 3-space

Abstract

Keywords

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