Important Group Theory Question Series | Q.1 🔥😍| Normal Subgroup #mathshorts #normalsubgroup

Added: 2026-05-22

[00:00:01]Hello everyone. So, welcome once again to my YouTube channel Maths and Life with Dr. Debojit Roy. From today onward, I'm going to start a series called important group theory questions for upcoming basic for semester examination.

[00:00:11]Uh in this series, I'm going to regularly post a question on each video.

[00:00:18]And you need to try those questions. The questions may be easy or questions may be hard. But you should at least give them a try. So, today in this video, uh I'm also going to provide a question which is associated with a important topic uh which is called normal subgroups. First, look at the question and read it and try to solve it, okay?

[00:00:41]So, first uh look at the question. The question is based on justify or invalidate a given statement, okay? So, first uh look at the question.

[00:00:50]Justify justify or invalidate invalidate the following the following the following statement.

[00:01:05]The following statement.

[00:01:08]And the statement is a group of a group of order 24 a group of order uh 24 does possess does possess does possess a normal a normal subgroup a normal subgroup of order order 14. So, you need to justify or invalidate this statement, okay?

[00:01:37]And if you were capable of justify or invalidate this given statement, so then you need to uh write your answer, okay? So, what you found uh in the comment box. So, again, uh I'm also going to provide you a hint so that you can uh try this question. And the hint which I'm going to giving you is that uh this question can be solved by using the Lagrange's theorem, okay? I hope everyone is familiar with Lagrange's theorem. And what is the statement of Lagrange's theorem?

[00:02:14]The statement of Lagrange's theorem says what? The order of the subgroup divides order of the group.

[00:02:21]By using this uh theorem, so you can solve it, okay?

[00:02:25]So, try it and then leave a comment on the comment box, okay? So, what do you found?

[00:02:31]So, thank you for visiting my YouTube channel.

[00:02:34]Keep watching my videos so that you can score better mark in your upcoming examination. Thank you.