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]
(..) It's only a shower. Besides, they got the infield covered. Say, could I see that knife a second, please? Well, we're still tied up six to six. Who's got a suggestion? - It's after . Let's get some dinner. - Why don't we wait till o'clock? OK with me. There's something I'd like to say. (..)1957 12 Angry Men