Prove that any element of a group can be expressed as a product of elements in a subset.
58654
If $|A| > \frac{|G|}{2} $ then $AA = G $
51697
Additive group contains exactly three elements of the set $\{p,p+q,pq,p^q,q^p\}$
19856
Prove that a subset of a separable set is itself separable
5089
An element of a group has the same order as its inverse
138670
If product of finite elements in a ring is a unit then can we say each element as unit
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
6153
Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
102971
Product of all elements of a finite group with an unique element of order 2
13355
Product of elements of a finite abelian group
129753
Prove that a subgroup which contains half of all elements is a normal subgroup.
31252
"Efficient version" of Cayley's Theorem in Group Theory
121423
Prove that every element of a finite group has an order
51896
Prove that: set $\{1, 2, 3, ..., n - 1\}$ is group under multiplication modulo $n$?
117658
A set with n elements has 2^n subsets
1409
Proving that the given set has at most $2^{n-1}$ elements
24181
Showing that $G$ is a group under an alternative operation.
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.