This is my question: Prove that there is no subgroup with size 6 in the symmetric group $A_4$.  What i thought is that $A_4$ has all the 2,4 circles,a subgroup with order 6 must be cyclic so there is no element in $A_6$ with order 6 so there is no subgroup with size 6.  I want to be sure that I am right,  thanks.
Show that  the  alternating  group  $A_4$  of all even permutations of $S_4$ does not contain a  subgroup of order $6$.   For me am thinking to write all elements of $A_4$ and trying to find every cyclic subgroup generated by each element of $A_4$, then I have to check whether there exist such a subgroup or not! This is a long procedure for me, I ask if there is a short way to do this.
I'm trying to process some data in Excel. The data includes numeric account numbers and other long numeric strings (like cell phone MEIDs). I am not doing math operations on these strings, so I want Excel to treat them as plain text.  Here is what is making me nuts (this is Excel 2010):   Take a long number like 1240800388917 and paste it in a cell in a new worksheet. Excel's default cell format is general, so the string is presented in scientific notation as 1.2408E+12 Right click on the cell, select Format Cells, set the format to Text   The cell is still displayed in scientific notation, even though the format has been set to text.  Now, if I do the steps in a different order:   Format an empty cell as text. Right click on the cell, select Format Cells, set the format to Text Take a long number like 1240800388917 and paste it in to the text formatted cell   Now, the cell is displayed as a string and not in scientific notation.  The results remaining in scientific notation even though the cell is formatted as text just seems broken to me. I've seen suggested work-arounds like: use CSV import and set the format to text, add a space character to the beginning of each numeric string, and others.  Is there a simple good work around to easily keep these strings formatted as text?  Why on earth does Excel do this?  Related SU questions I found:  and Given a dictionary like so:  my_map = {'a': 1, 'b': 2}   How can one invert this map to get:  inv_map = {1: 'a', 2: 'b'} Do harmonic numbers have a “closed-form” expression? Limit of $\prod\limits_{k=2}^n\frac{k^3-1}{k^3+1}$ Calculate $$\lim_{n \to \infty} \frac{2^3-1}{2^3+1}\times \frac{3^3-1}{3^3+1}\times \cdots \times\frac{n^3-1}{n^3+1}$$ No idea how to even start. How can I define a math operator behaving like \lim or \sum with limits? How do I delete a folder which is nested quite deep and avoid "File name too long"? 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