Solved: "How many subgroups of order 4 does D4..." - Plainmath

College
Algebra
Abstract algebra

nicekikah

Answered question

2020-12-15

How many subgroups of order 4 does

D_{4}

have?

Answer & Explanation

stuth1

Skilled2020-12-16Added 97 answers

We know that

D_{n}

is a dehedral group of order 2n. It is non-abelian group.
Therefore, the order of

D_{4}

is 8 and the list of elements is given by

D_{4} = {e, a, a^{2}, a^{3}, b, b a, b a^{2}, b a^{3}}

There are 3 subgroup of order in

D_{4}

which is given by

H_{1} = {e, a, a^{2}, a^{3}},

H_{2} = {e, b, a^{2}, b a^{2}}

H_{3} = {e, b a, a^{2}, b a^{3}}

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