Subgroup-closed lattice formations

Detecting the Index of a Subgroup in the Subgroup Lattice

A theorem by Zacher and Rips states that the finiteness of the index of a subgroup can be described in terms of purely lattice-theoretic concepts. On the other hand, it is clear that if G is a group and H is a subgroup of finite index of G, the index |G : H| cannot be recognized in the lattice L(G) of all subgroups of G, as for instance all groups of prime order have isomorphic subgroup lattice...

An El-labeling of the Subgroup Lattice

In a 2001 paper, Shareshian conjectured that the subgroup lattice of a finite, solvable group has an EL-labeling. We construct such a labeling and verify that our labeling has the expected properties.

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Surgery Obstructions on Closed Manifolds and the Inertia Subgroup

The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group In+1(π,w) and the closed manifold subgroup Cn+1(π,w) are equal in dimensions n+1 ≥ 6, for any finitely-presented group π and any orientation character w : π → Z/2. This answers a quest...

Closed Orbit Instability for Strong Focusing Lattice ∗

We extend analysis of Ref. [1] of the closed orbit instability driven by the resistive wall impedance for the case of strong focusing lattice. A numerical estimate for the Low Energy Ring of PEP-II shows that the threshold current is three times higher than the nominal one. ∗Work supported by Department of Energy contracts DE–AC03–76SF00515 and DE–AC02–76CH03000