proper subgroup sentence in Hindi

Examples

1. PGL is in general a proper subgroup of the collineation group.
2. The isometries form a proper subgroup of, namely PSU ( 2 ).
3. For, there are additional conditions, i . e . is then a proper subgroup of.
4. The Galois group of a polynomial of degree n is S _ n or a proper subgroup of that.
5. A subgroup of ? is called an " isolated subgroup " if it is a segment and is a proper subgroup.
6. Hence ? is induced from a character of a proper subgroup of " G " containing " N ."
7. There exist finite groups other than cyclic groups with the property that all proper subgroups are cyclic; the Klein group is an example.
8. Every proper subgroup of " G " can be assumed a solvable group, meaning that much theory of such subgroups could be applied.
9. In other words " H " is a maximal element of the partially ordered set of proper subgroups of " G ".
10. It is not possible for a finite group to be mapped by inclusion ( i . e . by a monomorphism ) as a proper subgroup of itself.