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Under vector addition α+β+γ=γ+β+α
is called the ____ law.
a.associative
b.distributive
c.commutative
d.Abelian
If x∗y= x+y+xy, find 2∗1?
a.5
b.2
c.3
d.4
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
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
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
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
Every cyclic group is
a.Commutative
b.Distributive
c.Multiplicative
d.Additive
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}\\)
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
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
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