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The intersection phi(G) of all maximal subgroups of a given group G.

The free product G*H of groups G and H is the set of elements of the form g_1h_1g_2h_2...g_rh_r, where g_i in G and h_i in H, with g_1 and h_r possibly equal to e, the ...

A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...

A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...

A distribution of values of a discrete variate represented graphically by plotting points (x_1,f_1), (x_2,f_2), ..., (x_k,f_k), and drawing a set of straight line segments ...