**Problem 1.** Let $ G $ be a group of permutations of a set $ S $, and let $ a \in S $. Prove that $ \text{stab}_G(a) $ is a subgroup of $ G $.This problem involves group theory, specifically focusing on permutations and subgroups. You must show that the stabilizer of an element $ a $ within the permutation group $ G $ is indeed a subgroup of $ G $.

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Problem 1. Let G be a group of permutations of a set S, and let a e S. Prove that stabg(a) is a subgroup of G.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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**Problem 1.** Let $ G $ be a group of permutations of a set $ S $, and let $ a \in S $. Prove that $ \text{stab}_G(a) $ is a subgroup of $ G $.

This problem involves group theory, specifically focusing on permutations and subgroups. You must show that the stabilizer of an element $ a $ within the permutation group $ G $ is indeed a subgroup of $ G $.

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