Comments on: Every Group of Order 72 is Not a Simple Group https://yutsumura.com/every-group-of-order-72-is-not-a-simple-group/ Fri, 19 Jan 2018 05:46:56 +0000 hourly 1 https://wordpress.org/?v=5.3.6 By: Yu https://yutsumura.com/every-group-of-order-72-is-not-a-simple-group/#comment-5051 Fri, 19 Jan 2018 05:46:56 +0000 https://yutsumura.com/?p=3280#comment-5051 Dear cb,

I added more explanations.

We know that $|G/\ker f|$ divides $|S_4|=2^3\cdot 3$. Note that $|G|=2^3 \cdot 3^2$. So if $\ker f$ does not contain the factor $3$, then $|G/\ker f|$ cannot divide $|S_4|=2^3\cdot 3$.

]]> By: cb https://yutsumura.com/every-group-of-order-72-is-not-a-simple-group/#comment-4954 Tue, 09 Jan 2018 20:49:57 +0000 https://yutsumura.com/?p=3280#comment-4954 Hi, i didn’t understand why do you say: “the order |kerf| is divisible by 3” ?

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