1. Examples Example 1.1. The field extension Q(√ 2, √ 3)/Q is Galois of degree 4, so its Galois group has order 4. The elements of the Galois group are determined by their values on √ 2 and √ 3. The Q-conjugates of √ 2 and √ 3 are ± √ 2 and ± √ 3, so we get at most four possible automorphisms in the Galois group. See Table 1. Since the Galois group has order 4, these 4 possible assignments of v...

In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order q ≥ 13 is 3q − 4 and describe all resolving sets of that size if q ≥ 23. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order q ≥ 4 is shown to fall between 2q−2 and 3q−6, while fo...

Let $G$ be a finite group and $pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ with vertex set $pi(G)$ and two distinct vertices $p$ and $q$ in $pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $psim q$. Let $|G= p_1^{alpha_1}cdot p_2^{alpha_2}cdots p_k^{alpha_k}$, where $p_1

In this paper we investigate qz/4-sets of type (O,q/4,q/2) in projective planes of order q=O(mod4). These sets arise in the investigation of regular triples with respect to a hyperoval. Combinatorial properties of these sets are given and examples in Desarguesian projective planes are constructed.

in this paper‎, ‎we propose a modification of the second order method‎ ‎introduced in [‎‎q. li and ‎x‎. ‎y. ‎wu‎, a two-step explicit $p$-stable method for solving second order initial value problems‎, ‎textit{‎appl‎. ‎math‎. ‎comput‎.}‎ {‎138}‎ (2003)‎, no. 2-3, ‎435--442‎] for the numerical solution of‎ ‎ivps for second order odes‎. ‎the numerical results obtained by the‎ ‎new method for some...