61 If I know the order of every element in a group, do I know the group? 35 Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal? 34 Prime numbers the rank of which is also a prime. 32 Complete classification of the groups for which converse of Lagrange's Theorem holds 24 If the field of a vector space weren't characteristic zero, then what would change in the theory?

### Reputation (85,647)

 +5 Largest determinant of a real $3\times 3$-matrix +10 Lie algebra of the general linear group in terms of the ABCDE classification? -2 Elimination of variables from a system of equation. +10 Subgroups of $D_4$

### Questions (7)

 16 Largest determinant of a real $3\times 3$-matrix 4 Examples of Dedekind rings with infinite class number 4 Solutions in positive integers of $a+b\mid ab+1$ and $a-b\mid ab-1$ 3 Are Mersenne numbers $M_p$ deficient? 3 Which integers are a product of partition numbers?

### Tags (528)

 2k abstract-algebra × 893 514 matrices × 245 1k group-theory × 579 478 elementary-number-theory × 217 1k number-theory × 553 472 finite-groups × 163 771 lie-algebras × 485 350 prime-numbers × 127 695 linear-algebra × 379 284 lie-groups × 162