Question

let H & K are two subgroup of Z144 of order 24 and 36 then what is the order of H intersection K​

Answer 1

Answer:

gcd (p,q).

Step-by-step explanation:

ohkk so what u need is a group which contains elements from both H and K.Now question is what kind of elements can H intersection K have?..obviously it must contain elements whose order divide both 24 and 36 and hence gcd (24,36)=12 must be the order of group note that since H and K are subgroups of a cyclic group Z144 and hence H intersection K is also a cyclic subgroup containing 12 elements. Now i will conclude my answer with few remarks

1.If G is cyclic subgroup and H and K are subgroups of G : o (H)=p and o (K)=q then

o (H intersection K) = gcd (p,q).

2.Above formulae will not work if G is not cyclic.

Answer 2

Step-by-step explanation:

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