MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

# P Vanchinathan

 741 Reputation 334 views

## Registered User

 Name P Vanchinathan Member for 1 year Seen 9 hours ago Website Location Chennai, India Age
 Jun3 answered General bound for the number of subgroups of a finite group May20 comment Permutations of $(Z/pZ)^*$What is the meaning of $a(i)-a(j)$ in the second paragraph of your question? Does it mean the function whose value at $k$ is $a(i)(k)-a(j)(k)$, using the subtraction in the ring $\mathbf{Z}/p\mathbf{Z}$. In that case,your condition (A) forces this to be a permutation. Then $a(i)$ and $a(j)$ are permutations agreeing nowhere. Is the map $a$ a group homomorphism? Then $a$ specifies a free action of $\mathbf{Z}/p\mathbf{Z}^*$ on itself. May19 comment Existence of nontrivial roots of a homogeneous polynomial over a finite field in extension fieldsMy answer given yesteray is wrong. One can choose $p$ variables to have non-zero value, and set all others to be zero to get a non-trivial solution. Should I delete it? May18 comment Existence of nontrivial roots of a homogeneous polynomial over a finite field in extension fieldsThe above is wrong. One can choose $p$ variables to have non-zero value, and set all others to be zero to get a non-trivial solution. I am sorry to have rushed in without fully verifying. May17 answered Existence of nontrivial roots of a homogeneous polynomial over a finite field in extension fields May15 awarded ● Necromancer May15 comment Possible ratios of Pythagorean fractionsAm I misreading the question? Do you want to know if $4/9$ is a RATIO of two Pythogorean fractions, as opposed to being a Pythagorean fraction by itself? The wording of your question means an expression for $4/9$ as $\frac{p_1q_1/(p_1^2-q_1^2)}{p_2q_2/(p_2^2-q_2^2)}$ is what is desired (using Barry Cipra's suggestion). May15 comment polynomial zero within a squareI see the snag. Can't we, with hindsight, specify values to be even higher at 1, $1+i$ so that scaling constant can't bring down. Of course this depends on the least absolute value of the zero. I'll try to rework again. Thanks, Johan! May14 answered polynomial zero within a square May14 comment Simplifying an algebraic integer expressionPerhaps you have more info that could reduce the degree. For example, the fields generated individually by $p_{41}$ and $p_{21}$ could intersect in a field of degree 16. and similar things.Also possibly a a convenient automorphism (a Galois group element) might send your number $p_4$ to a number more amenable for computations. May3 answered Does there exist a polar decomposition of matrices over finite fields? May1 answered Generate a higher degree symmetric polynomial from an existing one Apr29 comment The largest number of irreducible characters of the same degree in a finite groupHave no idea how to solve this problem. But do remember that M. Isaacs (author of a book on Character Theory) has written papers that have a lot to do with the set of character degrees. Apr14 awarded ● Yearling Apr11 comment Irreducible Degrees and the Order of a Finite Group Thanks, John for a clear writing. Apr11 answered Combined standard deviation Apr11 comment Is the Segre embedding projectively normal?More along this line: The cone over the Grassmannian for the Pl\"ucker embedding is even a factorial variety. (And quadratic relations among Pl\'ucker co-ordinates holds.) Book by Lakshmibai on 'Standard Monomial Theory' has more generalisations. Popov's generalisation: same is true for orbits of highest weight vectors in an irreducible representation of simply-connected semisimple algebraic group $G$ (over C?). Apr9 comment Irreducible Degrees and the Order of a Finite Group Correction to my earlier comment: I meant real two-dimensional representation for odd cyclic groups. Apr9 awarded ● Nice Question Apr8 comment Irreducible Degrees and the Order of a Finite Group @David Speyer: Thanks for the detailed answer here and at SE. I am teaching rep theory without using group algebras and fumbling. In Lagrange's theorem we see cosets are of same cardinality and provide a partition of $G$. About degree of intermediate fields in finite extensions also we have a transparent proof. I am looking for such a simple underlying idea. As odd ordered cyclic groups have 2-dimensional irreps as symmetries of regular polygons we need to bring the dependence on complex numbers (via Schur's lemma). Not that easy perhaps. :-( Apr8 comment A question from Otto Forster’s book on Riemann surfaces(TeX comment) Insert a missing dollar sign to make the question readable. Apr8 asked Irreducible Degrees and the Order of a Finite Group Apr1 answered Parabolic-type subgroups of GL(V) Mar26 answered Decomposition of solvable Lie group Mar21 answered 3D Rotation Representation for Multiple Turns Mar15 answered Subfield of rational function field and which is not a rational function field Mar9 awarded ● Critic Jan20 comment Minimum sum among fixed length factors of a numberThe equality connecting arithmetic mean and geometric mean should be relevant here. Jan19 awarded ● Enthusiast Jan12 answered The inverse Galois problem, what is it good for? Jan10 comment Quotients of rational surfacesFor $k=\mathbf{Q}$ work of Saltman,(retract rational) on Noether's problem could be relevant, and Swan, Lenstra for abelian groups. But all of them talk of higher dimensional varieties. Specifically cyclically permuting $n$ variables over $\mathbf{Q}$ does not give a fixed field that is purely transcendental for $n=47$ (Swan) and $n=8$ (Lenstra). Jan6 answered Does every polynomial diophantine equation have solutions modulo p? Jan3 awarded ● Commentator Jan3 comment Primitive Elements for $S_n$ Galois Extensions?Thanks to Elkies, and Swain. Your answers are clear and explicit and readily usable to construct. I have now my work cut out getting that polynomial of degree 24 giving $S_4$ as Galois extension. Jan3 comment Primitive Elements for $S_n$ Galois Extensions?Thanks Qiaochu: the opening paragraph was missed out during editing and I have restored it now. Jan3 revised Primitive Elements for $S_n$ Galois Extensions?Inserted part missed out in cut and paste Jan3 asked Primitive Elements for $S_n$ Galois Extensions? Jan3 awarded ● Scholar Jan2 comment How to apply Hilbert’s Irreducibilty theorem? Successful specialisation is ok. When a specialisation fails what exactly is the meaning? The polynomial fails to be irreducible? Or it remains irreducible but with different Galois group for the splitting field? I was under the impression that if a specilisation is irreducible then Galois group is the same. Jan2 asked How to apply Hilbert’s Irreducibilty theorem? Dec28 answered Is there a “geometric” intuition underlying the notion of normal varieties? Dec27 answered parabolic subgroup