Now lets discuss about the Second chapter named as SUBGROUPS . As mentioned before I am following the sequence of chapters from Herstein. IMPORTANT IDEAS: i) First go through the definition very well. You will see that H is a subgroup of G when H is a group under the...

Hello, this is a discussion page for the college students who are in various prestigious colleges throughout India, and are keen to pursue Mathematics. Abstract Algebra plays a pivotal role in college mathematics, and it mainly focuses on three things GROUPS, RINGS,...

QUESTION [NBHM(January)(2015) 1.1] Solve the following equation, given that it’s roots are in arithmetic progression: \[x^3-9x^2+28x-30 =0\] DISCUSSION: Now every root in the above mentioned equation is in arithmetic progression. So let the roots be a, a+d,...

Question: Is it possible to get an infinite group which has elements of finite order? Discussion To pursue this discussion which is basically a very good concept for the students who are new in group theory, they must know first about the QUOTIENT GROUPS. Particularly...

Problem (Artin, chapter 4, 7.1) Determine the Jordan form of a matrix $$ \left[ \begin{array}{ccc} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{array} \right] $$ Discussion According to the Jordan form of a matrix, we first determine the...