We show that the Sylow 2-subgroups of nearly all Chevalley groups in even characteristic allow the definition of a check-character-system which detects all single and the most important double errors.

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .

In this paper, we determine all of subgroups of symmetric group S4 by applying Lagrange theorem and Sylow theorem. First, we observe the multiplication table of S4, then we determine all possibilities of every subgroup of order n, with n is the factor of order S4. We found 30 subgroups of S4. The diagram of lattice subgroups of S4 is then presented. Mathematics Subject Classification: 20B30, 20...

Valuations on a field K are encoded in the absolute Galois group GK of K: They are in one-to-one correspondence to the conjugacy classes of decomposition subgroups of GK which (apart from few exceptions) can be characterized in group theoretic terms. Roughly speaking decomposition subgroups of GK are maximal subgroups of GK with a Sylow-subgroup containing a non-trivial abelian normal subgroup....