Answer both questions: • The quaternion group (Q, a) is a group of order 8 with two generators a and b subject to the relations a4 = e, b2 = a2, land a oboa= b. To be explicit, the •.) elements of Q...

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Answer both questions:
• The quaternion group (Q, a) is a group of order 8 with two generators a and b subject to the relations a4 = e, b2 = a2, land a oboa= b. To be explicit, the •.) elements of Q are e. a. a2, a3. b, a o b, a o b, a3 b. For this discussion prompt, research the subject and find an application of the quaternion group that differs from any of your peer's responses. Write the Cayley table. find the center. and find all cyclic subgroups for Q. • Find and present an example of a group not presented here or in your textbook that has some application in or outside of mathematics.

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Answer both questions: For question two of a present example of a group it can be Rubik's Cube group

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Answered Same DayDec 23, 2021

Answer To: Answer both questions: • The quaternion group (Q, a) is a group of order 8 with two generators a and...

Robert answered on Dec 23 2021

120 Votes

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We wil work with the standard notations i, j, k used for quaternion group. The quaternion group, or quaternionic
group, is a noncommutative group with eight elements. It is traditionally denoted by Q (not to be confused with Q)
or by Q8. This group is defined by the presentation
{i, j; i4, i2j2, iji−1j}
or, equivalently, defined by the multiplication table (Cayley table)
· 1 i j k −i −j −k −1
1 1 i j k −i −j −k −1
i i −1 k −j 1 −k j −i
j j −k −1 i k 1 −i −j
k k j −i −1 −j i 1 −k
−i −i 1 −k j −1 k −j i
−j −j k 1 −i −k −1 i j
−k −k −j i 1 j −i −1...

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Answer both questions: • The quaternion group (Q, a) is a group of order 8 with two generators a and b subject to the relations a4 = e, b2 = a2, land a oboa= b. To be explicit, the •.) elements of Q...

Answer To: Answer both questions: • The quaternion group (Q, a) is a group of order 8 with two generators a and...

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