Which alternating and symmetric groups are unit groups?
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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
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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