Let G be a finite group and α be an automorphism of G of order p n for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.

Theorem 1 gives an explicit formula for the heat kernel on an H -type group. Folland (2] has shown that for stratified nilpotent Lie groups the heat semigroup is a semigroup of kernel operators on LP, 1 5 p < oo and on Co. Cygan (1] has obtained formulas for heat kernels for any two step nilpotent simply connected Lie group. Cygan found the heat kernel for a free simply connected two step nilpo...

We study the residual properties of geometric 3–manifold groups. In particular, we study conditions under which geometric 3–manifold groups are virtually residually p for a prime p, and conditions under which they are residually torsion–free nilpotent. We show that for every prime p, every geometric 3–manifold group is virtually residually p. We show that geometric 3– manifold groups are virtua...

We study indigenous bundles in characteristic p > 0 with nilpotent p-curvature, and show that they corresponds to simpler objects which we call deformation data. We consider the existence problem of a certain class of deformation data, which arise from the reduction of Belyi maps from characteristic zero to characteristic p. Mathematics Subject Classification (2000): Primary 14H25, 14H60.

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...

1.1 We prove that: Over any field I of characteristic p > 0, there exists an infinite dimensional Lie algebra which is the join of two (p + l)-dimensional and nilpotent (of class exactly p) subideals. A result of Hartley ([2; p. 259, theorems 2 and 5]) states that over any field of characteristic zero, the join of a pair of finite dimensional (resp. finite dimensional and nilpotent) subideals i...

in this paper‎, ‎we investigate the influence of some subgroups of sylow subgroups with semi cover-avoiding property and‎ ‎$mathcal{f}$-supplementation on the structure of finite groups and generalize a series of known results‎.