Question

लेग्राज प्रमेय का कथन लिखिए एवं सिद्ध कीजिए।
State and prove Lagrange's theorem.

Answer 1

Answer:

Lagrange theorem is one of the central theorems of abstract algebra. It states that in group theory, for any finite group say G, the order of subgroup H of group G divides the order of G. The order of the group represents the number of elements. This theorem was given by Joseph-Louis Lagrange. In this article, let us discuss the statement and proof of Lagrange theorem in Group theory, and also let us have a look at the three lemmas used to prove this theorem with the examples.

As per the statement, the order of the subgroup H divides the order of the group G. This can be represented as;

|G| = |H|

Before proving the Lagrange theorem, let us discuss the important terminologies and three lemmas that help to prove this theorem.