The non-two-primes graph of a finite group

To any finite group G, we may associate a graph whose vertices are the elements of G and where two distinct vertices x and y are adjacent if and only if the order of the subgroup \langle x, y\rangle is divisible by at least ۳ distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most ۵.

کلیدواژه ها:

Finite groups ، order of elements ، graphs associated to finite groups