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2 | Part (A) was answered by another poster. | ||
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(B) is probably difficult since it is listed as an open problem in the book Profinite Groups by Ribes and Zalesski (2009). [Question 4.8.5b (p. 401): "Is a torsion profinite group necessarily of finite exponent?"] I think there is also a positive answer to (A) in that book, and maybe when I have more time I can say more about it. |
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(B) is probably difficult since it is listed as an open problem in the book Profinite Groups by Ribes and Zalesski (2009). [Question 4.8.5b (p. 401): "Is a torsion profinite group necessarily of finite exponent?"] I think there is also a positive answer to (A) in that book, and maybe when I have more time I can say more about it. |
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