Which alternating and symmetric groups are unit groups?

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Standard

Which alternating and symmetric groups are unit groups? / Davis, Christopher James; Occhipinti, Tommy.

I: Journal of Algebra and its Applications, Bind 13, 1350114, 2014.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Davis, CJ & Occhipinti, T 2014, 'Which alternating and symmetric groups are unit groups?', Journal of Algebra and its Applications, bind 13, 1350114. https://doi.org/10.1142/S0219498813501144

APA

Davis, C. J., & Occhipinti, T. (2014). Which alternating and symmetric groups are unit groups? Journal of Algebra and its Applications, 13, [1350114]. https://doi.org/10.1142/S0219498813501144

Vancouver

Davis CJ, Occhipinti T. Which alternating and symmetric groups are unit groups? Journal of Algebra and its Applications. 2014;13. 1350114. https://doi.org/10.1142/S0219498813501144

Author

Davis, Christopher James ; Occhipinti, Tommy. / Which alternating and symmetric groups are unit groups?. I: Journal of Algebra and its Applications. 2014 ; Bind 13.

Bibtex

@article{14a8ebab283444e294d3a3126b0aacd0,
title = "Which alternating and symmetric groups are unit groups?",
abstract = "We prove there is no ring with unit group isomorphic to Sn for n ≥ 5 and that there is no ring with unit group isomorphic to An for n ≥ 5, n \neq 8. To prove the non-existence of such a ring, we prove the non-existence of a certain ideal in the group algebra F_2[G], with G an alternating or symmetric group as above. We also give examples of rings with unit groups isomorphic to S1, S2, S3, S4, A1, A2, A3, A4, and A8. Most of our existence results are well-known, and we recall them only briefly; however, we expect the construction of a ring with unit group isomorphic to S4 to be new, and so we treat it in detail.",
author = "Davis, {Christopher James} and Tommy Occhipinti",
year = "2014",
doi = "10.1142/S0219498813501144",
language = "English",
volume = "13",
journal = "Journal of Algebra and its Applications",
issn = "0219-4988",
publisher = "World Scientific Publishing Co. Pte. Ltd.",

}

RIS

TY - JOUR

T1 - Which alternating and symmetric groups are unit groups?

AU - Davis, Christopher James

AU - Occhipinti, Tommy

PY - 2014

Y1 - 2014

N2 - We prove there is no ring with unit group isomorphic to Sn for n ≥ 5 and that there is no ring with unit group isomorphic to An for n ≥ 5, n \neq 8. To prove the non-existence of such a ring, we prove the non-existence of a certain ideal in the group algebra F_2[G], with G an alternating or symmetric group as above. We also give examples of rings with unit groups isomorphic to S1, S2, S3, S4, A1, A2, A3, A4, and A8. Most of our existence results are well-known, and we recall them only briefly; however, we expect the construction of a ring with unit group isomorphic to S4 to be new, and so we treat it in detail.

AB - We prove there is no ring with unit group isomorphic to Sn for n ≥ 5 and that there is no ring with unit group isomorphic to An for n ≥ 5, n \neq 8. To prove the non-existence of such a ring, we prove the non-existence of a certain ideal in the group algebra F_2[G], with G an alternating or symmetric group as above. We also give examples of rings with unit groups isomorphic to S1, S2, S3, S4, A1, A2, A3, A4, and A8. Most of our existence results are well-known, and we recall them only briefly; however, we expect the construction of a ring with unit group isomorphic to S4 to be new, and so we treat it in detail.

U2 - 10.1142/S0219498813501144

DO - 10.1142/S0219498813501144

M3 - Journal article

VL - 13

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

M1 - 1350114

ER -

ID: 64391862