Finite loops arising from projective 3-space

S. Pasotti; S. Pianta; E. Zizioli

doi:10.1007/s13366-017-0356-4

Finite loops arising from projective 3-space

S. Pasotti^*, S. Pianta, E. Zizioli

^*Corresponding author

Research output: Contribution to journal › Article › 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\r\nrelevant (maximal subgroups).

Original language	English
Pages (from-to)	155-165
Number of pages	11
Journal	Beitrage zur Algebra und Geometrie
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s13366-017-0356-4
Publication status	Published - 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

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

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10.1007/s13366-017-0356-4

Cite this

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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\r\nrelevant (maximal subgroups).",

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AU - Pasotti, S.

AU - Pianta, S.

AU - Zizioli, E.

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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\r\nrelevant (maximal subgroups).

KW - Left loop

KW - PGL_2(q)

KW - PSL_2(q)

KW - loop transversal

KW - Left loop

KW - PGL_2(q)

KW - PSL_2(q)

KW - loop transversal

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DO - 10.1007/s13366-017-0356-4

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SP - 155

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JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

IS - 1

ER -

Finite loops arising from projective 3-space

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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