Question

Show that the intersection of any number of subgroups of G is a subgroup of G

Answer 1

Sub-groups, super-groups and union groups are mathematical terms that arise from equations which can be solved by Venn diagrams. They often refer to a particular set or the part of a set which can be found in the universal set.

 

Assuming that there is a group denoted as G, it will have an infinite number of sub-groups. Each subgroup can either be independent or intersecting. The intersecting subgroups will form a new group inside the group G itself. We denote the new intersection as F. Thus, F will be the sub-group of group G.

 

Hence, the above statement is proved.

Answer 2

If P and Q are subgroups of a group G, it is to prove that intersection of P and Q is also a subgroup of G.

This is a problem in Algebra and it is true that intersection between two subgroups of G is also a subgroup of G.

The proof to this problem is given online in relevant sources.

Similarly the intersection of any number of subgroups of G is a subgroup of G.