Abstract Algebra: Theory and Applications · Problem 6.5.20

Introduction to Cryptography — Thomas Judson

Mathematics — Abstract Algebra · double-cosets

Problem

Let

H

and

K

be subgroups of a group

G

. Define a relation

\sim

G

a \sim b

if there exists an

h \in H

and a

k \in K

such that

hak = b

. Show that this relation is an equivalence relation. The corresponding equivalence classes are called double cosets. Compute the double cosets of

H = \{(1),(1\,2\,3),(1\,3\,2)\}

A_4