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Advanced Group Theory University of Galway - Engineering & Computer Science Program Spring 2023 Semester - Galway

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Advanced Group Theory

Advanced Group Theory Course 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


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

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