ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is t...
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| Format: | Article |
| Language: | English |
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Shahrood University of Technology
2018-09-01
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| Series: | Journal of Algebraic Systems |
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| Online Access: | http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf |
| _version_ | 1818836457525084160 |
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| author | Z. Sepehrizadeh M. R. Rismanchian |
| author_facet | Z. Sepehrizadeh M. R. Rismanchian |
| author_sort | Z. Sepehrizadeh |
| collection | DOAJ |
| description | In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic in G. We determine the upper and lower bounds for this probability. We also obtain a special lower bound, when H is a cyclic p-subgroup of G. |
| first_indexed | 2024-12-19T03:06:55Z |
| format | Article |
| id | doaj.art-d3185af2857f4ec9aa1d8b764ccfec2f |
| institution | Directory Open Access Journal |
| issn | 2345-5128 2345-511X |
| language | English |
| last_indexed | 2024-12-19T03:06:55Z |
| publishDate | 2018-09-01 |
| publisher | Shahrood University of Technology |
| record_format | Article |
| series | Journal of Algebraic Systems |
| spelling | doaj.art-d3185af2857f4ec9aa1d8b764ccfec2f2022-12-21T20:38:05ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2018-09-0161718010.22044/jas.2018.6328.13161256ON THE CHARACTERISTIC DEGREE OF FINITE GROUPSZ. Sepehrizadeh0M. R. Rismanchian1Department of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: zohreh.sepehri@gmail.comDepartment of Pure Mathematics, Shahrekord University , P.O.Box 115, Shahrekord, Iran. Email: rismanchian133@gmail.com, rismanchian@sku.ac.irIn this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic in G. We determine the upper and lower bounds for this probability. We also obtain a special lower bound, when H is a cyclic p-subgroup of G.http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdfautocommutativity degreecharacteristic degreep-group |
| spellingShingle | Z. Sepehrizadeh M. R. Rismanchian ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS Journal of Algebraic Systems autocommutativity degree characteristic degree p-group |
| title | ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS |
| title_full | ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS |
| title_fullStr | ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS |
| title_full_unstemmed | ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS |
| title_short | ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS |
| title_sort | on the characteristic degree of finite groups |
| topic | autocommutativity degree characteristic degree p-group |
| url | http://jas.shahroodut.ac.ir/article_1256_9cb3d15cf6327aa4481ad9fb54223403.pdf |
| work_keys_str_mv | AT zsepehrizadeh onthecharacteristicdegreeoffinitegroups AT mrrismanchian onthecharacteristicdegreeoffinitegroups |