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When was Hovhannes Abelian born?
Hovhannes Abelian was born in 1865.
When did Hovhannes Abelian die?
Hovhannes Abelian died in 1936.
Is every abelian group is cyclic or not and why?
every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
Is the symmetry group of the square an abelian group?
Abelian meaning commutative. If the symmetry group of a square is commutative then it's an abelian group or else it's not.
What is Abelian algebra?
Abelian algebra is a form of algebra in which the multiplication within an expression is commutative.
Is a group of order 24 abelian group or not?
The abelian groups of order 24 are C3xC8, C2xC12, C2xC2xC6. There are other 12 non-abelian groups of order 24
What is the definition of an abelian group?
An abelian group is a group in which ab = ba for all members a and b of the group.
Is every finite abelian group is cyclic?
No, for instance the Klein group is finite and abelian but not cyclic. Even more groups can be found having this chariacteristic for instance Z9 x Z9 is abelian but not cyclic
Is every abelian group is cyclic or not?
No.
Is every solvable group abelian?
No.
What is abelianization?
Abelianization is a homomorphism which transforms a group into an Abelian group.
Can a non-abelian group have a torsion subgroup?
Yes, a non-abelian group can have a torsion subgroup. A torsion subgroup is defined as the set of elements in a group that have finite order. Many non-abelian groups, such as the symmetric group ( S_3 ), contain elements of finite order, thus forming a torsion subgroup. Therefore, the existence of a torsion subgroup is not restricted to abelian groups.
