1. If H is a subgroup of a group G of index 2. show that H is a normal

1.	1. If H is a subgroup of a group G of index 2. show that H is a normal subgroup of G.
Answer» <html><body><p><strong>Step-by-step explanation:</strong></p><p>here we have to take 2 seperate <a href="https://interviewquestions.tuteehub.com/tag/case-910082" style="font-weight:bold;" target="_blank" title="Click to know more about CASE">CASE</a> </p><p>case <a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a> </p><p>a€H and a€G</p><p>case 2</p><p>a doesn't belong to H and a€G </p><p>In both cases we prove H is a normal sub <a href="https://interviewquestions.tuteehub.com/tag/group-1013370" style="font-weight:bold;" target="_blank" title="Click to know more about GROUP">GROUP</a> of G</p></body></html>

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