Is H a Normal Subgroup If Every Left Coset Equals a Right Coset?

Thread starter nbacombi
Start date Dec 7, 2010
Tags

Normal Normal subgroup Subgroup

Join the discussion

Registration is free. Start your own thread to ask a follow-up.

1 reply · 3K views

nbacombi

Thread starter
Dec 7, 2010

Let G be a group and H be a subgroup of G. If every left coset xH, where x in G, is equal to a right coset Hy, for some y in G, prove H is normal subgroup.

Help?

Physics news on Phys.org

Ultrathin materials could make quantum light circuits programmable
Spin rephasing helps quantum memories store single-photon states longer for future networks
Discovery confirms rare, switchable electrical property in widely used electronics material

Discussion

lanedance

Homework Helper

Dec 7, 2010

so what is the definition of normal subgroup?

Is H a Normal Subgroup If Every Left Coset Equals a Right Coset?

Discussion

Similar threads

Show group equivalence relation associated with normal subgroup

Proof that H is normal iff left cosets equal right cosets

Why does n times a coset equal the zero coset in Q/Z?

Proving something about right cosets of distinct subgroups of a group

Find Left Cosets of Subgroup in $\mathbb{Z}_{15}, D_4$

Graduate Is NH Always a Normal Subgroup of G When N and H Are Normal Subgroups?

Graduate Elements in only 1 left/right coset

Graduate Why is H a normal subgroup of its normalizer?

Graduate How to determine if a subgroup is normal in Group Theory?