means only identity element is there. right?

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Bikram
asked
in Set Theory & Algebra
Aug 8, 2016

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8 votes

Best answer

Lagrange's Theorem :

The order of a finite group is a multiple of the order of its every subgroup

Here Order of group is 11 which is Prime no. So only 2 subgroups are possible.

a. Group itself (i.e. Order 11)

b. Group with order 1

but both of above are Trivial Sub Group i.e. no Proper Sub Group possible from Prime Order Group.

0 votes

Order/cardinality of the group = 11.

Lagrange's theorem states that the order of every subgroup H of a group G, divides the order of G.

So what divides 11? 1 and 11.

Of order 1, there's only one subgroup, ie, {e} (identity element). This is the trivial subgroup. Every group has it.

Of order 11, the same group itself.

So, essentially there are no subgroups.

**Option A**