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Let G be a group and let G act on itself by conjugation. For a e G, denote Oa the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. Recall that the action by conjugation on G is given by ga = gag¬1, for g,a EG (Hint: Find the kernel for this particular action (by conjugation), not just any action.) a) Find the kernel of the induced permutation representation p: G → → Sf•

Let G be a group and let G act on itself by conjugation. For a e G, denote Oa the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. Recall that the action by conjugation on G is given by ga = gag¬1, for g,a EG (Hint: Find the kernel for this particular action (by conjugation), not just any action.) a) Find the kernel of the induced permutation representation p: G → → Sf•

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Im lost on this one for abstract algebra, please assist me. Action by conjugation

1.7. Let G be a group and let G act on itself by conjugation. For a E G, denote Og the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. Recall that the action by conjugation on G is given by ga = gag-1, for g, a e G (Hint: Find the kernel for this particular action (by conjugation), not just any action.) (a) Find the kernel of the induced permutation representation p: G – Sg.
Transcribed Image Text:1.7. Let G be a group and let G act on itself by conjugation. For a E G, denote Og the orbit of a under conjugation action. The orbits under the conjugation action are called the conjugacy classes of G. Recall that the action by conjugation on G is given by ga = gag-1, for g, a e G (Hint: Find the kernel for this particular action (by conjugation), not just any action.) (a) Find the kernel of the induced permutation representation p: G – Sg.
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