When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n > 2 such that an + bn = cn. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.

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Modular elliptic curves and Fermat’s Last Theorem

The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment. In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.

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Quantum error correction via codes over GF(4)

Modular Elliptic Curves and Fermat′s Last Theorem(抜粋) (フェルマ-予想がついに解けた!?)

General introduction to the special odd case General lemmas Theorem $C^*_2$: Stage 1 Theorem $C^*_2$: Stage 2 Theorem $C_2$: Stage 3 Theorem $C_2$: Stage 4 Theorem $C_2$: Stage 5 Theorem $C_3$: Stage 1 Theorem $C_3$: Stages 2 and 3 IV$_K$: Preliminary properties of $K$-groups Background references Expository references Glossary Index.

http://inis.jinr.ru/sl/M_Mathematics/MA_Algebra/MAtg_Group%20theory/Gorenstein%20D.,%20Lyons%20R.,%20Solomon%20R.%20Classification%20of%20finite%20simple%20groups%201%20(AMS%20survey%2040%20no.1,%201994,%202000)(176s).pdf

The Classification of the Finite Simple Groups

: This study considers a class of doubly transitive groups satisfying the condition that the identity is the only element leaving three distinct letters fixed. The main object of the investigation is to classify the groups which do not contain a regular normal subgroup of order 1 + N in case N is even. (Author)

On a class of doubly transitive groups

Endliche Gruppen I

Finite Groups II

Notations and results from group theory representations and representation-modules simple and semisimple modules orthogonality relations the group algebra characters of abelian groups degrees of irreducible representations characters of some small groups products of representation and characters on the number of solutions gm =1 in a group a theorem of A. Hurwitz on multiplicative sums of squares permutation representations and characters the class number real characters and real representations Coprime action groups pa qb Fronebius groups induced characters Brauer's permutation lemma and Glauberman's character correspondence Clifford theory 1 projective representations Clifford theory 2 extension of characters Degree pattern and group structure monomial groups representation of wreath products characters of p-groups groups with a small number of character degrees linear groups the degree graph groups all of whose character degrees are primes two special degree problems lengths of conjugacy classes R. Brauer's theorem on the character ring applications of Brauer's theorems Artin's induction theorem splitting fields the Schur index integral representations three arithmetical applications small kernels and faithful irreducible characters TI-sets involutions groups whose Sylow-2-subgroups are generalized quaternion groups perfect Fronebius complements. (Part contents).

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Bertram Huppert

Papers

Endliche Gruppen I

Finite Groups II

Character theory of finite groups

Normalteiler und maximale Untergruppen endlicher Gruppen

Zweifach transitive, auflösbare Permutationsgruppen