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A group is called a free group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

At rational arguments p/q, the digamma function psi_0(p/q) is given by psi_0(p/q)=-gamma-ln(2q)-1/2picot(p/qpi) +2sum_(k=1)^([q/2]-1)cos((2pipk)/q)ln[sin((pik)/q)] (1) for ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be geometric if ac=b^2. In particular, such a triple is geometric if its terms form a geometric sequence ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

A Hajós group is a group for which all factorizations of the form (say) Z_n=A direct sum B have A or B periodic, where the period is a divisor of n. Hajós groups arose after ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

Define F(1)=1 and S(1)=2 and write F(n)=F(n-1)+S(n-1), where the sequence {S(n)} consists of those integers not already contained in {F(n)}. For example, F(2)=F(1)+S(1)=3, so ...