We present the hglm package for fitting hierarchical generalized linear models. It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects. Fixed effects can also be fitted in the dispersion part of the model.

For a finite group G and an arbitrary prime p, let S (G) denote the P intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set S (G) G. Some properties of P G are considered involving S (G). In particular, we obtain a characterization of P G when each M in the definition of S (G) is nilpotent. P

Definitions and classifications of reduced surds for non-arithmetical groups on the hyperbolic plane is proposed, as well those some congruence subgroups. The considered are desymmetrized group, its Γ0 subgroup, a generalized Hecke group according choice commutator subgroup group. definitions studied to ordering generators conjugacy subclasses groups. construction tori defined obtained after te...

Root-class residuality of free product of root-class residual groups is demonstrated. A sufficient condition for root-class residuality of generalized free product G of groups A and B amalgamating subgroups H and K through the isomorphism φ is derived. For the particular case when A = B, H = K and φ is the identity mapping, it is shown that group G is root-class residual if and only if A is roo...

Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...

A subgroup H of a group G is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is called weakly s-permutable in G if there is a subnormal subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We fix in every non-cyclic Sylow subgr...