On subgroups and equivalent relations
Date of Publication
1998
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
This paper is an exposition of "Subgroups and Equivalence Relations", by Pierre J. Malraison, Jr. (1977). It contains key results detailing the relationship between subgroups and equivalence relations. The results were obtained using the concepts of group action and commutator groups. 1) If G is a group and R is an equivalence relation on G, the following are equivalent: (i) R is closed under products in G x G; (ii) R is a subgroup of G x G; (iii) R is the relation of belonging to the same coset of some normal subgroup of G. 2) If the equivalence relation R is a subgroup of G x G, then the following are equivalent: i) R is normal in G x G. ii) G/[e] is abelian. iii) G' is a subgroup of [e].
Abstract Format
html
Language
English
Format
Accession Number
TU08767
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
54 leaves
Keywords
Group actions (Mathematics); Algebraic varieties; Topological transformation groups; Equivalence relations (Set theory)
Recommended Citation
Baysic, C., & Chen Cen Sio, D. T. (1998). On subgroups and equivalent relations. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/16496
