On a symmetry criterion for conjugacy infinite groups
This study is an exposition of the article entitled On a Symmetry Criterion for Conjugacy in Finite Groups by W. Jacobson. It is shown that two elements a and b of a finite group G are conjugates if and only if they can be found symmetrically situated relative to the main diagonal of the group table...
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Main Authors: | , |
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Format: | text |
Language: | English |
Published: |
Animo Repository
1998
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Subjects: | |
Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16499 |
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Institution: | De La Salle University |
Language: | English |
Summary: | This study is an exposition of the article entitled On a Symmetry Criterion for Conjugacy in Finite Groups by W. Jacobson. It is shown that two elements a and b of a finite group G are conjugates if and only if they can be found symmetrically situated relative to the main diagonal of the group table. Moreover, if a and b are conjugate elements of a finite group G with a # b, then there are n/k = r pairs of elements {ui, Vi] in G X G such that uiVi = and viui=b, where n is the order of G, and k is the size of the conjugacy class in G to which a and b belong. |
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