Decomposable and indecomposable algebras of degree $$8$$ 8 and exponent 2

groups of order $p^8$ and exponent $p$

we prove that for $p>7$ there are‎ ‎[‎ ‎p^{4}+2p^{3}+20p^{2}+147p+(3p+29)gcd (p-1,3)+5gcd (p-1,4)+1246‎ ‎] ‎groups of order $p^{8}$ with exponent $p$‎. ‎if $p$ is a group of order $p^{8}$‎ ‎and exponent $p$‎, ‎and if $p$ has class $c>1$ then $p$ is a descendant of $‎p/gamma _{c}(p)$‎. ‎for each group of exponent $p$ with order less than $‎p^{8} $ we calculate the number of descendants of o...

r-Indecomposable and r-Nearly Decomposable Matrices

Let n, r be integers with 0 ≤ r ≤ n− 1. An n×n matrix A is called r-partly decomposable if it contains a k×l zero submatrix with k+l = n−r+1. A matrix which is not r-partly decomposable is called r-indecomposable (shortly, r-inde). Let Eij be the n × n matrix with a 1 in the (i, j) position and 0’s elsewhere. If A is r-indecomposable and, for each aij 6= 0, the matrix ∗Research supported by Nat...

Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras

For a Del Pezzo surface of degree 8 given over the rationals we decide whether there is a rational parametrization of the surface and construct one in the affirmative case. We define and use the Lie algebra of the surface to reach the aim. The algorithm has been implemented in Magma.

GENERIC ALGEBRAS WITH INVOLUTION OF DEGREE 8 mDavid

00 8 Indecomposable Pd 3 - Complexes

We show that if the fundamental group π of an inde-composable orientable P D 3-complex is the fundamental group of a finite graph of finite groups then the vertex groups have periodic cohomology and the edge groups are metacyclic. If the vertex groups all have cohomological period dividing 4 at most one is not dihedral, the edge groups are Z/2Z, and the underlying graph is a tree. We also ask w...