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How to get maximum number of groups from some ''n'' elements so that no two groups have more than one element in common and no restriction on size of the group .

j s s
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  • What elements? Where do you get them? If you just want groups with $n$ elements, than I can give you infinitely many that have no intersection, simply by using different names for the elements every time.

    Or are you interested in the isomorphism classes of groups of $n$ elements? In this case: abelian or also non-abelian?

     – Dirk Apr 12 '17 at 11:28
  • In mathematics, the word group means a set together with a binary operation that is associative, closed under inverses, and has an identity element. Did you mean group in the formal sense or a subset? – N. F. Taussig Apr 12 '17 at 12:33
  • It's the usual grouping idea , all i am trying to get is an upper bound for number of groups possible to ''n'' number of element . I have tried for 10 elements when i take a group of size 9 then total groups possible with those 10 elements with at most one element in common is only 10 . – j s s Apr 13 '17 at 03:49
  • You have the empty set; $n$ subsets of size $1$, and $n\choose2$ subsets of size $2$. – Empy2 May 30 '18 at 11:59

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