Is there a particular characterization of Aut(Q3)?

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anita1415snck · Accepted Answer

Step 1A vector space over Q is the same as a torsionfree divisible abelian group. The product pq×v is the unique vector so that q×pqv=pv.In particular, every group homomorphism between vector spaces over Q is automatically Q-linear. Thus, for example, the group automorphisms of Qn may be described by GLn(Q).

coesarfaujs3t · Accepted Answer

The distinction between preserving addition and also preserving scalar multiplication is illusory in this case, because any vector can be divided by n.The distinction resurfaces, however, for the same problem with Q replaced by (almost) any other field, such as the real numbers. There preserving scalar multiplication is an additional property that does not follow from addition being conserved.

Is there a particular characterization of \(\displaystyle{A}{u}{t}{\left({\mathbb{{{Q}}}}^{{3}}\right)}\)?

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