Telegram group: T.me/BBCNOUN
[MTH312] \(A_{n}\), the group of even permutations in \(S_{n}\), is called___________
alternating group of degree \(n \)

[MTH312] If \(f, g \in S_{n}\) are odd, then \(f\dot g) is ___________
prime

[MTH312] One of these is not algebraic structure of group G if G is an Abelian group of order 8
\( Z_{2^{3}}\)

[MTH312] An isomorphism onto itself is called __________________
Automorphism

[MTH312] Let \(o(G) =p^{2}\), then G is Abelian if \(p\) is ___________
prime

[MTH312] In the theory of permutations, 2-cycles are called ___________
Transpositions

[MTH312] The identity permutation is ___________________
even

[MTH312] Express (1 3 5) cycle as product of transpositions
(1 5)(1 3)

[MTH312] What is the signature of \(1\in S_{n}\)
1

[MTH312] A group G is called simple if it has only normal subgroups
{e} and G itself