On the ESQ Property of Certain Representations of Metacyclic Groups
A group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$. We investigate whether $F_{p,q}$ has an irreducible represe...
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| Format: | Article |
| Language: | English |
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Aracne
2017-06-01
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| Series: | Advances in Group Theory and Applications |
| Subjects: | |
| Online Access: | http://www.advgrouptheory.com/journal/Volumes/4/J.%20Wolosz%20-%20On%20the%20ESQ%20property%20of%20certain%20representations%20of%20metacyclic%20groups.pdf |
| _version_ | 1798044064426229760 |
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| author | János Wolosz |
| author_facet | János Wolosz |
| author_sort | János Wolosz |
| collection | DOAJ |
| description | A group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$. We investigate whether $F_{p,q}$ has an irreducible representation with the ESQ property. Fixing one of the parameters $q$ or $p−1$, we will be able to give an asymptotic answer to this question. |
| first_indexed | 2024-04-11T22:57:39Z |
| format | Article |
| id | doaj.art-b5942e65e964434a84ba3d9f13bf8760 |
| institution | Directory Open Access Journal |
| issn | 2499-1287 2499-1287 |
| language | English |
| last_indexed | 2024-04-11T22:57:39Z |
| publishDate | 2017-06-01 |
| publisher | Aracne |
| record_format | Article |
| series | Advances in Group Theory and Applications |
| spelling | doaj.art-b5942e65e964434a84ba3d9f13bf87602022-12-22T03:58:21ZengAracneAdvances in Group Theory and Applications2499-12872499-12872017-06-014839010.4399/97888255086976On the ESQ Property of Certain Representations of Metacyclic GroupsJános Wolosz0ELTE Eötvös Loránd UniversityA group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$. We investigate whether $F_{p,q}$ has an irreducible representation with the ESQ property. Fixing one of the parameters $q$ or $p−1$, we will be able to give an asymptotic answer to this question.http://www.advgrouptheory.com/journal/Volumes/4/J.%20Wolosz%20-%20On%20the%20ESQ%20property%20of%20certain%20representations%20of%20metacyclic%20groups.pdfmetacyclic groupFermat type equation |
| spellingShingle | János Wolosz On the ESQ Property of Certain Representations of Metacyclic Groups Advances in Group Theory and Applications metacyclic group Fermat type equation |
| title | On the ESQ Property of Certain Representations of Metacyclic Groups |
| title_full | On the ESQ Property of Certain Representations of Metacyclic Groups |
| title_fullStr | On the ESQ Property of Certain Representations of Metacyclic Groups |
| title_full_unstemmed | On the ESQ Property of Certain Representations of Metacyclic Groups |
| title_short | On the ESQ Property of Certain Representations of Metacyclic Groups |
| title_sort | on the esq property of certain representations of metacyclic groups |
| topic | metacyclic group Fermat type equation |
| url | http://www.advgrouptheory.com/journal/Volumes/4/J.%20Wolosz%20-%20On%20the%20ESQ%20property%20of%20certain%20representations%20of%20metacyclic%20groups.pdf |
| work_keys_str_mv | AT janoswolosz ontheesqpropertyofcertainrepresentationsofmetacyclicgroups |