HOMEWORKS
Homework 6
Which of the following groups are isomorphic: all real numbers subject to
addition, all nonzero real numbers subject to multiplication, all positive
real numbers subject to multiplication?
Homework 9
It is known that the map \(x \mapsto x^{-1}\) is an automorphism of a group.
What can be said about this group?
Homework 11
Is it true that the automorphism group of an abelian group is abelian?
Homework 12
Prove that if \(N \triangleleft G\) and \(M \triangleleft H\), then
\((N \times M) \triangleleft (G \times H)\). What can be said about the quotient
\((G \times H) / (N \times M)\)?
Homework 15
Is the relation "to be a normal subgroup of a group" transitive?
Homework 20
Classify, up to isomorphism, algebras with unit of dimension 2 over the field
of complex numbers.
Created: Mon Feb 12 2024
Last modified: Tue Apr 8 2025 16:50:59 CEST