he centers of Sylow 2-subgroups form a single conjugacy class. In particular, by Lemmas 1.1, 2.4 and 3.7 of [3], the group PSp(4, 3) has exactly two classes of involutions, say t and u and |CPSp(4,3)(t)| = …
ns and A7 is the unique simple group with 105 involutions. Added in Proof. The . roups At and PSL(3, 4) are of the same order and each has 315 involutions. Conjecture: if two simple g. s. me. nu. ber of …
ON Abstract. Answering a question of Geo Robinson, we compute the large n limiting proportion of iGL(n; q)=qbn2=2c, where iGL(n; q) denotes the number of involutions. in GL(n; q). We give similar …
In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 pub-lished paper, disproved Herzog’s conjecture with a …
sylow theory - A question about the involution in simple ...
Example: PSL (3,4) has a single class of involutions, and its centralizer is the Sylow 2-subgroup. PSp (4,4) has three classes of involutions (all central), and ONE of the classes has centralizer a Sylow 2 …
An infinitude of counterexamples to Herzog's conjecture on ...
Now it is natural to ask whether or not any nonabelian simple group can be determined by the conditions in Moretó's conjecture together with the number of involutions. ...
Hence the Baer involu-tions (involutions in P L(3; 4) P GL(3; 4) whose xed points are a Baer subplane) are not central in P GL(3; 4) or P SL(3; 4) and the group P L(3; 4) interchanges two of these classes.