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Advanced Group Theory
University of Galway - Direct Enroll Program
Galway, Ireland
Dates: early Jan 2026 - mid May 2026
Advanced Group Theory
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA4344
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
The course covers monoids and groups and their actions. Topics covered include finite state machines, orbits and stabilizers, applications in combinatorics (e.g. vertex colorings), Sylow theory, finite simple groups.
Learning Outcomes
1. Define monoid actions; state and prove fundamental theorems about them
2. Determine regular languages for finite automata
3. Use orbit-stabilizer theory to compute automorphism groups of graphs
4. State and prove Sylow's theorems
5. Prove there is no finite non-abelian simple group of order less than 60
Learning Outcomes
1. Define monoid actions; state and prove fundamental theorems about them
2. Determine regular languages for finite automata
3. Use orbit-stabilizer theory to compute automorphism groups of graphs
4. State and prove Sylow's theorems
5. Prove there is no finite non-abelian simple group of order less than 60