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Abstract Algebra
Under vector addition α+β+γ=γ+β+α
is called the ____ law.
a.associative
b.distributive
c.commutative
d.Abelian
is called the ____ law.
a.associative
b.distributive
c.commutative
d.Abelian
Abstract Algebra
If x∗y= x+y+xy, find 2∗1?
a.5
b.2
c.3
d.4
a.5
b.2
c.3
d.4
Abstract Algebra
If S is a subset of a group G, then the smallest subgroup of G containing S is called the _____ by the set S.
a.coset generated
b.abelian generated
c.product generated
d.subgroup generated
a.coset generated
b.abelian generated
c.product generated
d.subgroup generated
Abstract Algebra
Let A and B be two subgroups of a group G. Prove that A
cup B is a subgroup of G iff_____.
a.A\\(\\subseteq\\) B
b.B\\(\\subseteq\\) A
c.A\\(\\subseteq\\) B and B\\(\\subseteq\\) A
d.A\\(\\subseteq\\) B or B
cup B is a subgroup of G iff_____.
a.A\\(\\subseteq\\) B
b.B\\(\\subseteq\\) A
c.A\\(\\subseteq\\) B and B\\(\\subseteq\\) A
d.A\\(\\subseteq\\) B or B
Abstract Algebra
Which of the following listed below a subgroup of G, if H and K are two subgroups of a group G?
a.H\\(\\mathrm{\\cap}\\)K
b.H/K
c.H-K
d.H\\(\\cup\\)K
a.H\\(\\mathrm{\\cap}\\)K
b.H/K
c.H-K
d.H\\(\\cup\\)K
Abstract Algebra
The set Z left (Gright) =left g in G:xg=gxfor all x in Gright is called ______
a.element
b.order
c.coset
d.centre
a.element
b.order
c.coset
d.centre
Abstract Algebra
Every cyclic group is
a.Commutative
b.Distributive
c.Multiplicative
d.Additive
a.Commutative
b.Distributive
c.Multiplicative
d.Additive
Abstract Algebra
1.Let G be a group. Then left (ab right)^−1=______ for every A in G.
a.\\(b^{-1}a^{-1}\\)
b.\\(Ab\\)
c.\\(ba\\)
d.\\(A^{-1}b^{-1}\\)
a.\\(b^{-1}a^{-1}\\)
b.\\(Ab\\)
c.\\(ba\\)
d.\\(A^{-1}b^{-1}\\)
Abstract Algebra
list all groups of order 2, and
a)determine whether the groups are cyclic or not
b)determine whether the groups are abelian or not
c)list down all the subgroups and normal subgroups of the groups
d)list down if the groups are isomorphic to other groups
a)determine whether the groups are cyclic or not
b)determine whether the groups are abelian or not
c)list down all the subgroups and normal subgroups of the groups
d)list down if the groups are isomorphic to other groups
Abstract Algebra
for groups of order 1,
a)determine whether the groups are cyclic or not
b)determine whether the groups are abelian or not
c)list down all the subgroups and normal subgroups of the groups
d)list down if the groups are isomorphic to other groups
a)determine whether the groups are cyclic or not
b)determine whether the groups are abelian or not
c)list down all the subgroups and normal subgroups of the groups
d)list down if the groups are isomorphic to other groups
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