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\begin{document}

\title{
Exam for ``Algebraic Structures'' (6ALGS) 
\\ 
summer semester 2023/2024
}

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\section*{Questions set no. 8}

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\textbf{1.} 

Formulate and prove the second and third homomorphism theorems for algebras.

\vskip 20pt 

\textbf{2.}

Is it true that any group satisfying the condition
\\
a) $x^2 = 1$
\\
b) $x^3 = 1$
\\
for any element $x$ of the group, is abelian?

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\textbf{3.}

Give example of a group whose group of inner automorphisms is isomorphic to
$\mathbb Z / 2\mathbb Z$, and the group of all automorphisms is isomorphic to
$\mathbb Z / 3\mathbb Z$.

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