Suppose that is a group acting on and that is a group homomorphism. Prove that acts on by the rule .
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Originally Posted by joestevens Suppose that is a group acting on and that is a group homomorphism. Prove that acts on by the rule . It pretty much falls out if you just follow the definition. What are you having trouble with?
Definition: acts on if there exists a function such that i) for ii) . Should I use i & ii above as the definition of the group action on and show also acts on by ? Am I to take as a subgroup of or is just any group?
Originally Posted by joestevens Definition: acts on if there exists a function such that i) for ii) . Should I use i & ii above as the definition of the group action on and show also acts on by ? Am I to take as a subgroup of or is just any group? Just use that definition. For example, i) is satisfied since
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