Kurukshetra university Msc Maths

Hi buddy want admission in Kurukshetra university Msc Maths program so would you plz tell me Kurukshetra university Maths program syllabus here ???

Kurukshetra university Department of Mathematics came into existence in the year 1961.

As you want here I am providing Kurukshetra university Msc Maths program syllabus :


Semester – I
MM-401: Advanced Abstract Algebra-I
Examination Hours : 3 Hours
Max. Marks : 100
(External Theory Exam. Marks:80
+ Internal Assessment Marks:20)
NOTE :
The examiner is requested to set nine questions in all taking two
questions from each section and one compulsory question. The compulsory question
will consist of eight parts and will be distributed over the whole syllabus. The
candidate is required to attempt five questions selecting at least one from each
section and the compulsory question.
Section – I (Two Questions)
Automorphisms and Inner automorphisms of a group G. The groups Aut(G) and Inn(G).
Automorphism group of a cyclic group. Normalizer and Centralizer of a non-empty
subset of a group G. Conjugate elements and conjugacy classes. Class equation of a finite
group G and its applications. Derived group (or a commutator subgroup) of a group G.
perfect groups. Zassenhau’s Lemma. Normal and Composition series of a group G.
Scheier’s refinement theorem. Jordan Holder theorem. Composition series of groups of
order pn and of Abelian groups. Caunchy theorem for finite groups. ∏ - groups and p-
groups. Sylow ∏-subgroups and Sylow p-subgroups. Sylow’s Ist, IInd and IIIrd
theorems. Application of Sylow theory to groups of smaller orders.
Section – II (Two Questions)
Characteristic of a ring with unity. Prime fields Z/pZ and Q. Field extensions. Degree of
an extension. Algebraic and transcendental elements. Simple field extensions. Minimal
polynomial of an algebraic element. Conjugate elements. Algebraic extensions. Finitely
generated algebraic extensions. Algebraic closure and algebraically closed fields.
Splitting fields., finite fields.. Normal extensions.
Section – III (Two Questions)
Separable elements, separable polynomials and separable extensions. Theorem of
primitive element. Perfect fields. Galois extensions. Galois group of an extension.
Dedekind lemma Fundamental theorem of Galois theory. Frobenius automorphism of a
finite field. Klein’s 4-group and Diheadral group. Galois groups of polynomials.
Fundamental theorem of Algebra

Kurukshetra university Msc Maths syllabus

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