# Question related to order of groups [duplicate]

This question already has an answer here:

Given $A$ is a subset of grouo $G$ and $|A|>|\frac{G}{2}|$. How do i prove that each element of $G$ is product of rwo elements of $A$? I don't know where to begin, a hint would be very helpful.

## marked as duplicate by Derek Holt group-theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jul 31 '17 at 7:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

## 1 Answer

Hint: If $A$ is any subset of $G$, show that $g\in G$ is a product of two elements of $A$ if and only if $$A\cap\{a^{-1}g\mid a\in A\}\neq\emptyset.$$