Starters book in Algebra continued

Starters book in Algebra continued

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...

Starters hand book in Abstract Algebra

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,...
NBHM 2015 some algebra questions’ solution

NBHM 2015 some algebra questions’ solution

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,...
A Common but deadly question in Group theory

A Common but deadly question in Group theory

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...
Jordan form of a matrix

Jordan form of a matrix

ProblemĀ (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...