Abstract Algebra: Theory and Applications · Problem 6.5.12

Introduction to Cryptography — Thomas Judson

Mathematics — Abstract Algebra · cosets-lagrange-theorem

Problem

ghg^{-1} \in H

for all

g \in G

and

h \in H

, show that right cosets are identical to left cosets. That is, show that

gH = Hg

for all

g \in G

. Hint. Let

g_1 \in gH

. Show that

g_1 \in Hg

and thus

gH \subset Hg