Which of the following statements are true, and which short proof or a counter-example.
i)There is no non-abelian group of 12
ii)If in a group G every element is of finite order, then G is a finite order.
iii)The homomorphic image of a non-cyclic group is non cyclic.
iv) If a is an integral domain, then R /I is an integral domain for every non-zero ideal I of R .
v)If I and J are ideals of a ring R, then so is I U J
i) False alternating group is a non abelian group of order 12.
ii) False: is an infinite group with every element of finite order.
iii) False given by This is a homomorphism . The homomorphic image of non cyclic is the cyclic group
(iv) False. Take R= and I= . not an integral domain.
(v) False. Take R=, I= J= But not ideal, since but . So for an ideal must belong to it.
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