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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
THEORY OF GROUPS	MAT4461		0 + 0	3.0	6.0

Prerequisites

None

Language of Instruction	English
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals	Get knowledge about basic isomorphism theorems, simple groups and their characterizations, to construct a new group, divisible groups, group decompositions, free groups and finitely generated free abelian groups, direct and semi-direct product of groups, inner automorphisms, outer automorphisms, characteristic subgroups, normalizations, series, composition series, normal and subnormal series, finite groups, maximal subgroups, minimal subgroups, solvable subgroups, super solvable subgroups, Frattini subgroups, nilpotent groups.
Course Content	Basic isomorphism theorems, Simple groups, Characterizations of simple groups, To construct a new group, Divisible groups, Group decompositions, Free groups, Finitely generated free abelian groups, direct product of groups, semi-direct product of groups, inner and outer automorphisms, composion series, normal and subnormal series, Nilpotent groups
Learning Outcomes	1) Knows basic isomorphism theorems for groups 2) Determine whether given groups are isomorphic by using basic isomorphism theorems. 3) Construct semi-direct product of groups and find out relation these groups and direct product of these groups.