MathCastle
Groups and FieldsMediumThe Sylow Theorems

The Sylow Theorems · Medium problem

A group of order 5050 has an abelian Sylow 55-subgroup isomorphic to Z25\mathbb Z_{25} (cyclic, not Z5×Z5\mathbb Z_5\times\mathbb Z_5). How many elements of GG have order exactly 55?