Group Theory

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E0117/: Estimates how many Abelian subgroups are needed to cover a group in which every set of more than n elements contains two distinct commuting elements.

E0543/: Asks whether the number of random elements of an abelian group of order N whose subset sums cover it is at most log base two of N plus a small error.

E1098/: Concerns the non-commuting graph of a group, whose vertices are the group elements and whose edges join pairs that do not commute.

E1160/: Asks whether the number of groups of order n is at most the number of groups of order two to the m whenever n is at most two to the m.

E1161/: Determines for which orders k the number of permutations of n letters having order exactly k is largest.

E1162/: Asks for an asymptotic formula for the number of subgroups of the symmetric group on n letters, and for statistical results on their orders.

E1163/: Asks for a statistical description of the arithmetic structure of the orders of subgroups of the symmetric group on n letters.

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Combinatorial problems about groups, including non-commuting graphs of groups; exact coverings of a group by cosets are filed with covering systems.

Site tags routed here: group theory, number theory.