Normal Supercharacter Theory
There are three main constructions of supercharacter theories for a group G. The first, defined by Diaconis and Isaacs, comes from the action of a group A via automorphisms on our given group G. Another general way to construct a supercharacter theory for G, defined by Diaconis and Isaacs, uses the...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6397/pdf |
| _version_ | 1827323933907484672 |
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| author | Farid Aliniaeifard |
| author_facet | Farid Aliniaeifard |
| author_sort | Farid Aliniaeifard |
| collection | DOAJ |
| description | There are three main constructions of supercharacter theories for a group G. The first, defined by Diaconis and Isaacs, comes from the action of a group A via automorphisms on our given group G. Another general way to construct a supercharacter theory for G, defined by Diaconis and Isaacs, uses the action of a group A of automor- phisms of the cyclotomic field Q[ζ|G|]. The third, defined by Hendrickson, is combining a supercharacter theories of a normal subgroup N of G with a supercharacter theory of G/N . In this paper we construct a supercharacter theory from an arbitrary set of normal subgroups of G. We show that when we consider the set of all normal subgroups of G, the corresponding supercharacter theory is related to a partition of G given by certain values on the central primitive idempotents. Also, we show the supercharacter theories that we construct can not be obtained via automorphisms or a single normal subgroup. |
| first_indexed | 2024-04-25T02:00:32Z |
| format | Article |
| id | doaj.art-61c7ee70a72e4e2c82bdd76012b5a17a |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:32Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-61c7ee70a72e4e2c82bdd76012b5a17a2024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63976397Normal Supercharacter TheoryFarid Aliniaeifard0Department of Mathematics and Statistics [Toronto]There are three main constructions of supercharacter theories for a group G. The first, defined by Diaconis and Isaacs, comes from the action of a group A via automorphisms on our given group G. Another general way to construct a supercharacter theory for G, defined by Diaconis and Isaacs, uses the action of a group A of automor- phisms of the cyclotomic field Q[ζ|G|]. The third, defined by Hendrickson, is combining a supercharacter theories of a normal subgroup N of G with a supercharacter theory of G/N . In this paper we construct a supercharacter theory from an arbitrary set of normal subgroups of G. We show that when we consider the set of all normal subgroups of G, the corresponding supercharacter theory is related to a partition of G given by certain values on the central primitive idempotents. Also, we show the supercharacter theories that we construct can not be obtained via automorphisms or a single normal subgroup.https://dmtcs.episciences.org/6397/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Farid Aliniaeifard Normal Supercharacter Theory Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Normal Supercharacter Theory |
| title_full | Normal Supercharacter Theory |
| title_fullStr | Normal Supercharacter Theory |
| title_full_unstemmed | Normal Supercharacter Theory |
| title_short | Normal Supercharacter Theory |
| title_sort | normal supercharacter theory |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6397/pdf |
| work_keys_str_mv | AT faridaliniaeifard normalsupercharactertheory |