Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let G be an finite group. Consider the group ring C[G] := {ΣgeGagg: ag € C}. The addition is given by (ΣgeG ª99) + (ΣgeGbgg) := ΣgeG (ag+bg)g and the multiplica- tion is given by Show that N := (Σagg) (Σbnh) := ΣΙΣ agn-1bn)g. gEG heG gEG heG ΣgeGagg € C[G] : ΣgeG ag = 0} is an ideal of C[G]. What is C[G]/N?

Let G be an finite group. Consider the group ring C[G] := {ΣgeGagg: ag € C}. The addition is given by (ΣgeG ª99) + (ΣgeGbgg) := ΣgeG (ag+bg)g and the multiplica- tion is given by Show that N := (Σagg) (Σbnh) := ΣΙΣ agn-1bn)g. gEG heG gEG heG ΣgeGagg € C[G] : ΣgeG ag = 0} is an ideal of C[G]. What is C[G]/N?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Let G be an finite group. Consider the group ring C[G] := {ΣgeGagg: ag € C}. The addition is given by (ΣgeG 999) + (ΣgeGbgg) := ΣgeG (ag+bg)g and the multiplica- agg) tion is given by Show that N := (Σagg) (Σ bnh) := ΣΙΣagh-bn)g. -1 gEG hЄG gEG heG { ΣgeGª99 € C[G] : ΣgeGag=0} is an ideal of C[G]. What is C[G]/N?
Transcribed Image Text:Let G be an finite group. Consider the group ring C[G] := {ΣgeGagg: ag € C}. The addition is given by (ΣgeG 999) + (ΣgeGbgg) := ΣgeG (ag+bg)g and the multiplica- agg) tion is given by Show that N := (Σagg) (Σ bnh) := ΣΙΣagh-bn)g. -1 gEG hЄG gEG heG { ΣgeGª99 € C[G] : ΣgeGag=0} is an ideal of C[G]. What is C[G]/N?
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS