If #H# and #K# is subgroup of #G# and #|H|=10,|K|=49# then how do you find #|HnnK|# ?

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Answer 1 · 2018-02-22T07:13:53

#abs(H nn K) = 1#

The order of any element of a group must be a divisor of the order of that group.

Given:

#abs(H) = 10#

we can deduce that any element of #H# has order #1, 2, 5# or #10#.

Given:

#abs(K) = 49#

we can deduce that any element of #K# has order #1, 7# or #49#

So any element of #H nn K# has order in #{ 1, 2, 5 } nn { 1, 7, 49 } = { 1 }#.

That is: the only element of #H nn K# is the identity.