Mathematics Homework Solutions
#128957
Prove a subgroup is normal if and only if it is the union of conjugacy classes.
Let G be a group and let H be a subgroup of G. Prove that H is normal if and only if it is the union of conjugacy classes.
It is proven that a subgroup is normal if and only if it is the union of conjugacy classes. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
What is this?
By OTA - Overall OTA Rating
Departed OTA
Purchase Cost Now
$2.19 CAD (was ~$11.97)
Included in Download
- Plain text response
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Subgroups - If K is a subgroup of H and H is a subgroup of G, is K a subgroup of G? Please justify your answer.
- Group Theory : If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G. - If N is a normal subgroup of G and H is any subgroup of G, prove that NH is a subgroup of G.
- Group Theory : If H is a subgroup of G and N is a normal subgroup of G, show that H∩N is a normal subgroup of H. - If H is a subgroup of G and N is a normal subgroup of G, show that H∩N is a normal subgroup of H.
- Group Theory If H is a subgroup of G, let N(H) = {gєG|gHg^-1 = H}. Prove that if H is a normal subgroup of the subgroup K in G, then K is subset N(H)( that is, N(H) is the largest subgroup of G in which H is normal). - If H is a subgroup of G, let N(H) = {gєG|gHg^-1 = H}. Prove that if H is a normal subgroup of the subgroup K in G, then K is subset N(H)( that is, N(H) is the largest subgroup of G in wh ...
- Modern normal subgroups - if H is a subgroup of G, and K is a normal subgroup of G, prove that H K is a subgroup of G
