$LetGandHbe groups, andϕ:G→Ha group homomorphism. IfH_{1}is anormal subgroup ofH,prove thatϕ_{−1}(H_{1}),the preimage ofH_{1}underϕ,is anormal subgroup ofG. $

begin{array}{l}{text { Let } G text { and } H text { be groups, and } phi : G rightarrow H text { a group homomorphism. If } H_{1} text { is a }} \ {text { normal subgroup of } H, text { prove that } phi^{-1}left(H_{1}right), text { the preimage of } H_{1} text { under } phi, text { is a }} \ {text { normal subgroup of } G .}end{array}

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in order to prove ϕ − 1 ( H 1 ) is normal subgroup of... View the full answer