Show that the identity permutation cannot be expressed as the product of an odd number of transpositions.
134989
Prove that if the identity is written as the product of $r$ transpositions, then $r$ is an even number
140190
Binary operation $xy$, has identity, but not associativity. Is the inverse unique?
87238
$(1 2)(3 4)$ does not commute with any nonidentity element of odd order in $A_5$.
103784
Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
6204
How many permutations of $\{1, \ldots, n\}$ exist such that none of them contain $(i, i+1)$ (as a sequence) for $i \in {1,...,(n-1)}$?
37331
Prove that every set with more than one element has a permutation without fixed points
31421
Transpose inverse automorphism is not inner
70688
How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups?
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
142888
Why, intuitively, is the order reversed when taking the transpose of the product?
29084
Largest integer that can't be represented as a non-negative linear combination of $m, n = mn - m - n$? Why?
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
143293
Does every non-trivial subgroup of $S_9$ containing an odd permutation necessarily contain a transposition?
154133
Flawed proof by induction that $a^{n-1}=1$
25744
Multiplication in Permutation Groups Written in Cyclic Notation
28452
Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity