This work covers the maximal and prime ideals of the incidence algebra, derivations and
isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions …

The Iwasawa L-function L^/k of K/k is derived from the S-truncated Z-adic Artin L-functions
and belongs to the above group Horn*. The equivariant" main conjecture" asserts that there …

A quotient of a poset P is a partial order obtained on the equivalence classes of an
equivalence relation  on P;  is then called a congruence if it satisfies certain conditions …

Let G be a finite group. The table of marks of G arises from a characterization of the
permutation representations of G by certain numbers of fixed points. It provides a compact …

We study a Markov chain on generating n-tuples of a fixed group which arises in algorithms
for manipulating finite groups. The main tools are comparison of two Markov chains on …

Abstract The Cohen–Lenstra–Martinet heuristics predict the frequency with which a fixed
finite abelian group appears as an ideal class group of an extension of number fields, for …

For a finite group G and a finite set A, we study various algebraic aspects of cellular
automata over the configuration space A^ G AG. In this situation, the set CA (G; A) CA (G; A) …

The M\" obius function for a group, $ G $, was introduced in 1936 by Hall in order to count
ordered generating sets of $ G $. In this paper we determine the M\" obius function of the …

Let G be a finite group and pa prime divisor of IGI. Sylow's third theorem says that the
number of Sylow p-subgroups of G is congruent to 1 modulo p. This was generalized by …

In this paper, we investigate the block with a cyclic hyperfocal subgroup and abelian
quotient group of a defect group with respect to this hyperfocal subgroup. First, in the light of …