Another way to do this is to use individual elements. Take an element from {2, 6} and an element from {3, 7} and add them. Find the coset that contains the sum. That coset is the sum of the cosets. For example, if I use 6 from {2, 6} and 3 from {3, 7}, I get 6 + 3 = 1, which is in {1, 5}. Therefore, {2, 6}+ {3, 7} = {1, 5}. What happens if you choose different elements? Take 2 from {2, 6} and 7...

We apply Voronoi’s algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple Q-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.

We study some properties of interval-valued fuzzy normal subgroups of a group. In particular, we obtain two characterizations of interval-valued fuzzy normal subgroups. Moreover, we introduce the concept of an interval-valued fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal “infinitesimal subgroup” G such that the quotient G/G, equipped with the “logic topology”, is a compact (real) Lie group. Our first result is that the functor G 7→ G/G sends exact sequences of definably compact groups into exacts sequences of Lie group...