I'm shocked at the 'suggestion' that he deliberately cheated. = The very 'suggestion' that he deliberately cheated is shocking (to me).
They were careful to avoid any 'suggestion' of impropriety. [=avoid doing anything that could be seen as improper]
There was some 'suggestion' of swelling around his ankle. [=his ankle appeared to be slightly swollen]
(..) - Will you get it, please? - Ash, go with him. - No, no. I can manage, Ash. Don't follow me. Ash? Any suggestions from you or Mother? No, we're still collating. You're what? You're still collating? (..)1979 Alien