Number of non-isomorphic groups of square-free order $n$

Asked Mar 20 '15 at 02:59

Active Feb 06 '16 at 20:13

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$G$ is a group of order $n=p_1p_2....p_k$ then how to find the number of non-isomorphic groups of order $n$ where $p_i's$ are distinct primes

I can find the number of number of non-isomorphic abelian groups if $G$ has order of this type but how to proceed if $G$ is given to be any group?

Has any research been done in this direction?Where can I find it?

edited Feb 06 '16 at 20:13

pjs36

asked Mar 20 '15 at 02:59

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Related question here: http://math.stackexchange.com/questions/491408/given-any-n-in-mathbbn-how-many-non-isomorphic-groups-are-there – Newb Mar 20 '15 at 03:02
Try looking up groups of squarefree order. Here's something (not really exactly what you are looking for but in the same direction) – Eoin Mar 20 '15 at 03:03
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Note, you have two different usages of $n$ above. Probably want $n=p_1\cdots p_k$. – Thomas Andrews Mar 20 '15 at 03:05
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There's also this reference, that seems to imply that such groups are, in some sense, well understood. Do you mean original research, or does just understanding a rather deep result count as research? – pjs36 Mar 20 '15 at 04:10
@ThomasAndrews I have edited my question regarding $n$ – Learnmore Mar 20 '15 at 15:00
I mean original research @pjs36 – Learnmore Mar 20 '15 at 15:01
See http://oeis.org/A000001 and http://oeis.org/wiki/Number_of_groups_of_order_n. – lhf Apr 10 '15 at 13:41

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