isomorphic group meaning in Hindi

Examples

1. This group is also known as, and also as the isomorphic group.
2. Discrete normal subgroups play an important role in the theory of covering groups and locally isomorphic groups.
3. Tietze transformations are built up of elementary steps, each of which individually rather evidently takes the presentation to a presentation of an isomorphic group.
4. This fact is based on the Mostow rigidity theorem, that two isomorphic groups generated by reflections in H n for n > = 3, define congruent fundamental domains ( Vinberg polytopes ).
5. The exponential mapping is ( in this context ), after all, a map from a Lie algebra to the connected group generated by it, not to another isomorphic group or some quotient.
6. However, a significant difference with respect to the case of integer factorization is that such " building blocks " do not necessarily determine uniquely a group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution.
7. One obtains an isomorphic group ( indeed, a conjugate subgroup of GL ( " V " ) ) by replacing " ? " with any symmetric matrix with " p " positive eigenvalues and " q " negative ones ( such a matrix is necessarily nonsingular ); equivalently, any quadratic form with signature.
8. :Here's a cheap attack : given the Axiom of Choice, both R and C are themselves rational vector spaces of equal dimension, so they are isomorphic groups in particular, and since the group C has a C-vector space structure, so does R . But I wouldn't be at all surprised if it were impossible to actually " define " such a structure.