hi a little help would be kindly appreciated here guys.

any suggestions on how to go about doing these?

INFORMATION

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if K,Q are groups is a homomorphism the semi direct product is defined as follows.

(i) as a set

(ii) the group operation * is

THE QUESTION

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Verify formally that is a group and find a formula for in terms of and

-----> to show that it is a group, i know i have to show that the 4 conditions for being a group (e.g. associativity, closure, existance of identity element, existance of inverse) have to be satisfied. but not really too sure how to show it.. and im completely baffled for the 2nd part of the question.

please help out thnx