(2) Let G be a finite group with no element of order 3, and let a EG. (a) Can 3 divide o(a)? Either prove that it cannot or give an example where it does. (b) Must there exist an element x E G with x3...

(2) Let G be a finite group with no element of order 3, and let a EG.<br>(a) Can 3 divide o(a)? Either prove that it cannot or give an example where it does.<br>(b) Must there exist an element x E G with x3<br>a? Either prove that there must or give an example where<br>there is not.<br>(c) Must there exist an element y E G with y? = a? Either prove that there must or give an example where<br>there is not.<br>

Extracted text: (2) Let G be a finite group with no element of order 3, and let a EG. (a) Can 3 divide o(a)? Either prove that it cannot or give an example where it does. (b) Must there exist an element x E G with x3 a? Either prove that there must or give an example where there is not. (c) Must there exist an element y E G with y? = a? Either prove that there must or give an example where there is not.

Jun 04, 2022

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(2) Let G be a finite group with no element of order 3, and let a EG. (a) Can 3 divide o(a)? Either prove that it cannot or give an example where it does. (b) Must there exist an element x E G with x3...

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