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The Feit-Thompson conjecture asserts that there are no primes p and q for which (p^q-1)/(p-1) and (q^p-1)/(q-1) have a common factor. Parker noticed that if this were true, ...

The Fermat quotient for a number a and a prime base p is defined as q_p(a)=(a^(p-1)-1)/p. (1) If pab, then q_p(ab) = q_p(a)+q_p(b) (2) q_p(p+/-1) = ∓1 (3) (mod p), where the ...

For any sequence of integers 0<n_1<...<n_k, there is a flag manifold of type (n_1, ..., n_k) which is the collection of ordered sets of vector subspaces of R^(n_k) (V_1, ..., ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

The eccentricity epsilon(v) of a graph vertex v in a connected graph G is the maximum graph distance between v and any other vertex u of G. For a disconnected graph, all ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

The radius of a graph is the minimum graph eccentricity of any graph vertex in a graph. A disconnected graph therefore has infinite radius (West 2000, p. 71). Graph radius is ...

The upper central series of a group G is the sequence of groups (each term normal in the term following it) 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... that is constructed in the ...