The groups of order $2^m$ which contain an invariant cyclic subgroup of order $2^{m - 2}$

THE GROUPS OF ORDER pm WHICH CONTAIN EXACTLY p CYCLIC SUBGROUPS OF ORDER

If a group ( G ) of order pm contains only one subgroup of order pa, a > 0, it is known to be cyclic unless both p = 2 and at = l.f In this special case there are two possible groups whenever m > 2. The number of cyclic subgroups of order pa in G is divisible by p whenever G is non-cyclic and p > 2. J In the present paper we shall consider the possible types of G when it is assumed that there a...

ELLIPTIC EQUATIONS OF ORDER 2m IN ANNULAR DOMAINS

In this paper we study the existence of positive radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions. We consider a nonlinearity which is either sublinear or the sum of a sublinear and a superlinear term.

Mathema Tics: G. A. Miller Groups in Which Every Subgroup of Composite Order Is Invariant By

THE ORDER GRAPHS OF GROUPS

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...

The Bogdanov-Takens bifurcation study of 2m coupled neurons system with 2m+1$2m+1$ delays

In this paper the Bogdanov-Takens (BT) bifurcation of an 2m coupled neurons network model with multiple delays is studied, where one neuron is excitatory and the next is inhibitory. When the origin of the model has a double zero eigenvalue, by using center manifold reduction of delay differential equations (DDEs), the second-order and third-order universal unfoldings of the normal forms are ded...