dw14-6 This is Daily Work 14. Current Students: Enter your BSU email address to receive a copy of your responses. Let \(\phi \colon G \to H \) be an isomorphism between the groups \(G\) and \(H\).Which of the following is not necessarily true? \( \phi \) sends identity to identity. The inverse of \( \phi(x) \) is \( \phi(x^{-1}) \). If \( |G|=k \), then \(H\) has an element of order \(k\). The order of \( \phi(g) \) is equal to the order of \(g\). Which of the following observations would guarantee that \(G\) is not isomorphic to \(H\) ? If \(G\) is a subgroup of \(H\). If \(G\) and \(H\) have different operations. If \(G\) has 4 distinct subgroups and \(H\) has 8. If \(G\) and \(H\) are both infinite groups. If \(a \in G\) is not the identity element, and \(H\) is a subgroup of \(G\), which of the following sets is guaranteed to also be a subgroup of \(G\)? \( aH = \{ ax \colon x \in H \} \) \( Ha = \{ xa \colon x \in H \} \) \( aHa = \{ axa \colon x \in H \} \) \( aHa^{-1} = \{ axa^{-1} \colon x \in H\} \) Related