The main result of this work is an explicit construction of p-local subgroups of the Monster, the largest sporadic simple group. The groups constructed are the normalizers in the Monster of certain subgroups of order 32 , 52 , and 72 and have shapes 32+5+10-(Af11 xGL(2, 3)), 52+2+4-(S3xGL(2, 5)), and 72+1+2 • GL(2, 7). These groups result from a general construction which proceeds in three step...

A square matrix $A$ is an involution if $A^{2} = I$. The centralizer of a $S$ denoted by $\mathscr{C}(S)$ the set all such that $AS SA$ over algebraically closed field characteristic not equal to 2. We determine necessary and sufficient conditions for $A \in \mathscr{C}(S)$ be product involutions in where basic Weyr with homogeneous structure length 3. Finally, we will show some results case wh...