Some concepts about mathematics


Biswajit Biswas

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Let (G,o) be a semigroup containing a finite number of elements in which both the cancellation laws hold.Then (G,o) is a group.

9 months ago (edited) | [YT] | 1

Biswajit Biswas

Let G be a group and H be a normal sub-group of G and g be an element of G such that order of g is 55. Then the possible order of gH in G/H is :

9 months ago | [YT] | 2

Biswajit Biswas

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Let (G,o) be a semigroup and for any two elements a,b in G , each of the equation aox=b and yoa=b has a solution in G. Then (G,o) is a group.

9 months ago (edited) | [YT] | 4

Biswajit Biswas

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If G be a finite group and H be a normal sub-group of G , then order of an element gH in G/H is a divisor of the order of g in G.

9 months ago | [YT] | 3

Biswajit Biswas

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If G be a noncommutative group with center Z , then the quotient group G/Z is noncyclic.

9 months ago (edited) | [YT] | 3

Biswajit Biswas

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Centraliser of an element 'a' of a group G , C(a) is a subgroup of the group G.
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10 months ago (edited) | [YT] | 4

Biswajit Biswas

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Centre of a group G , Z(G) - is a subgroup of the group G .
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10 months ago (edited) | [YT] | 3

Biswajit Biswas

Next video is coming on the topic ::
If H be a subgroup of a cyclic group G , then the quotient group G/H is cyclic.
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10 months ago | [YT] | 4

Biswajit Biswas

Next video is coming on the topic::
Quotient Group: Let H be a normal subgroup of a group G. Then the set of all distinct cosets of H in G forms a group with respect to the binary operation * defined by, aH*bH=abH ; for all a,bโˆˆG .
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1 year ago | [YT] | 4

Biswajit Biswas

Next video is coming on the topic::
Let H be a subgroup of G. Then H is normal in G iff for hโˆˆH and xโˆˆG โ‡’ xhxโปยนโˆˆH .
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1 year ago | [YT] | 2