TY - JOUR
AU - Asche, David S.
AB - By DAVID S. ASCHE [Received 19 October 1967] 1. Introduction There have been investigations made recently of groups G which contain an involution t such that the centralizer C (t) has the form (ty x F where F is isomorphic to one of the projective special linear groups PSL(2, q) ((4) (5) (6)). In this paper we consider the effect of replacing the group (ty by an arbitrary dihedral group A and we prove the following theorem. THEOREM. Let G be a finite group with the following two properties: (a) The group G is perfect. (b) There is an involution t in G such that the centralizer H = C (t) contains a Sylow 2-subgroup of G and H = AxF where A is a dihedral group (of order d) and F is isomorphic to PSL(2, q) with q odd. Then there is a subgroup E of G such that A c E,G = ExF and E/O(E) is isomorphic to PSL(2,r) with r > 3 odd. (Also q > 3 and d is an odd multiple of r + e with e= ±1.) [Notation: O(E) denotes the unique maximal normal odd-order subgroup of E.] 2. Some known results We 
TI - Some Finite Groups of Even Order
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-19.2.208
DA - 1969-04-01
UR - https://www.deepdyve.com/lp/wiley/some-finite-groups-of-even-order-ObR5HeTkx7
SP - 208
EP - 218
VL - s3-19
IS - 2
DP - DeepDyve
ER -