Finite simple groups of low 2-rank and the families $G_2 \left ( q \right ), D_4^2 \left ( q \right ), q$ odd
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- by Daniel Gorenstein and Koichiro Harada PDF
- Bull. Amer. Math. Soc. 77 (1971), 829-862
References
- J. H. Conway, A group of order $8,315,553,613,086,720,000$, Bull. London Math. Soc. 1 (1969), 79β88. MR 248216, DOI 10.1112/blms/1.1.79
- Marshall Hall Jr., Simple groups of order less than one million, J. Algebra 20 (1972), 98β102. MR 285603, DOI 10.1016/0021-8693(72)90090-7
- Donald G. Higman and Charles C. Sims, A simple group of order $44,352,000$, Math. Z. 105 (1968), 110β113. MR 227269, DOI 10.1007/BF01110435
- Graham Higman and John McKay, On Jankoβs simple group of order $50,232,960$, Bull. London Math. Soc. 1 (1969), 89β94; correction, ibid. 1 (1969), 219. MR 246955, DOI 10.1112/blms/1.1.89
- Zvonimir Janko, A new finite simple group with abelian Sylow $2$-subgroups and its characterization, J. Algebra 3 (1966), 147β186. MR 193138, DOI 10.1016/0021-8693(66)90010-X
- Zvonimir Janko, Some new simple groups of finite order. I, Symposia Mathematica (INDAM, Rome, 1967/68) Academic Press, London, 1969, pp.Β 25β64. MR 0244371
- Richard Lyons, Evidence for a new finite simple group, J. Algebra 20 (1972), 540β569. MR 299674, DOI 10.1016/0021-8693(72)90072-5
- Jack McLaughlin, A simple group of order $898,128,000$, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp.Β 109β111. MR 0242941 8. C. Sims, On Lyons simple group of order 28•37•56•7•11•31•37•67 (to appear).
- Terence M. Gagen, On groups with abelian Sylow $2$-groups, Math. Z. 90 (1965), 268β272. MR 191963, DOI 10.1007/BF01158567
- Marshall Hall Jr. and David Wales, The simple group of order $604,800$, J. Algebra 9 (1968), 417β450. MR 240192, DOI 10.1016/0021-8693(68)90014-8
- David Parrott and S. K. Wong, On the Higman-Sims simple group of order $44,352,000$, Pacific J. Math. 32 (1970), 501β516. MR 257216
- R. G. Stanton, The Mathieu groups, Canad. J. Math. 3 (1951), 164β174. MR 40304, DOI 10.4153/cjm-1951-021-6
- S. K. Wong, On a new finite non-abelian simple group of Janko, Bull. Austral. Math. Soc. 1 (1969), 59β79. MR 269734, DOI 10.1017/S0004972700041290
- Paul Fong, A characterization of the finite simple groups $\textrm {PSp}(4.\,q),\,G_{2}\,(q),\,D_{4}{}^{2}\,(q)$. II, Nagoya Math. J. 39 (1970), 39β79. MR 288176
- Paul Fong and W. J. Wong, A characterization of the finite simple groups $\textrm {PSp} (4,q)$, $G_{2}(q)$, $D_{4}{}^{2}(q)$. I, Nagoya Math. J. 36 (1969), 143β184. MR 255666 16. M. Harris, A characterization of the simple groups $\textrm {PSp}(4\,q)$, q odd (to appear). 17. M. Harris, A characterization of the simple groups $\textrm {PSp}(4\,q),\,G_{2}\,(q),\,D_{4}{}^{2}\,(q)$, qodd(to appear).
- Dieter Held, A characterization of the alternating groups of degrees eight and nine, J. Algebra 7 (1967), 218β237. MR 218444, DOI 10.1016/0021-8693(67)90057-9
- Dieter Held, A characterization of some multiply transitive permutation groups. I, Illinois J. Math. 13 (1969), 224β240. MR 238944
- Takeshi Kondo, A characterization of the alternating group of degree eleven, Illinois J. Math. 13 (1969), 528β541. MR 246956
- Zvonimir Janko, A characterization of the Mathieu simple groups. I, II, J. Algebra 9 (1968), 1-19; ibid. 9 (1968), 20β41. MR 0229710, DOI 10.1016/0021-8693(68)90002-1
- Zvonimir Janko and S. K. Wong, A characterization of the Higman-Sims simple group, J. Algebra 13 (1969), 517β534. MR 260866, DOI 10.1016/0021-8693(69)90114-8 23. Z. Janko and S. Wong, A characterization of the McLaughlin simple group(to appear).
- Kok-wee Phan, A characterization of four-dimensional unimodular groups, J. Algebra 15 (1970), 252β279. MR 258977, DOI 10.1016/0021-8693(70)90077-3 25. K. Phan, A characterization of simple groups U(to appear).
- W. J. Wong, A characterization of the finite projective symplectic groups $\textrm {PSp}_{4}(q)$, Trans. Amer. Math. Soc. 139 (1969), 1β35. MR 252504, DOI 10.1090/S0002-9947-1969-0252504-X
- W. J. Wong, A characterization of the finite simple groups $\textrm {PSp}_{6}\,(q),\,q$ odd, J. Algebra 12 (1969), 494β524. MR 241528, DOI 10.1016/0021-8693(69)90025-8 28. R. Brauer, A characterization ofSz (8) (unpublished).
- Richard Brauer and Paul Fong, A characterization of the Mathieu group ${\mathfrak {M}}_{12}$, Trans. Amer. Math. Soc. 122 (1966), 18β47. MR 207817, DOI 10.1090/S0002-9947-1966-0207817-1
- Daniel Gorenstein and Koichiro Harada, A characterization of Jankoβs two new simple groups, J. Fac. Sci. Univ. Tokyo Sect. I 16 (1969), 331β406 (1970). MR 283075
- Daniel Gorenstein and Koichiro Harada, On finite groups with Sylow $2$-subgroups of type $A_{n}$, $n=8,\,9,\,10,\,11$, Math. Z. 117 (1970), 207β238. MR 276348, DOI 10.1007/BF01109844
- Daniel Gorenstein and Koichiro Harada, On finite groups with Sylow $2$-subgroups of type $\hat A$ $_{n},\,n=8,\,9,\,10,$ and $11$, J. Algebra 19 (1971), 185β227. MR 285599, DOI 10.1016/0021-8693(71)90104-9
- Daniel Gorenstein and Koichiro Harada, Finite groups whose Sylow $2$-subgroups are the direct product of two dihedral groups, Ann. of Math. (2) 95 (1972), 1β54. MR 313384, DOI 10.2307/1970852
- Daniel Gorenstein and Koichiro Harada, Finite groups with Sylow $2$-subgroups of type $\textrm {PSp}(4,$ $q),\,q$ odd, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 341β372. MR 338162
- Helmut Bender, On groups with abelian Sylow $2$-subgroups, Math. Z. 117 (1970), 164β176. MR 288180, DOI 10.1007/BF01109839
- Zvonimir Janko and John G. Thompson, On a class of finite simple groups of Ree, J. Algebra 4 (1966), 274β292. MR 201504, DOI 10.1016/0021-8693(66)90041-X
- John G. Thompson, Toward a characterization of $E_{2}^{\ast } (q)$, J. Algebra 7 (1967), 406β414. MR 223448, DOI 10.1016/0021-8693(67)90080-4
- Harold N. Ward, On Reeβs series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62β89. MR 197587, DOI 10.1090/S0002-9947-1966-0197587-8
- John H. Walter, The characterization of finite groups with abelian Sylow $2$-subgroups, Ann. of Math. (2) 89 (1969), 405β514. MR 249504, DOI 10.2307/1970648 40. H. Bender, Doubly transitive groups with no involution fixing two points(to appear). 41. H. Bender, Finite groups having a strongly embedded subgroup(to appear). 42. Z. Janko, Nonsolvable finite groups all of whose 2-local subgroups are solvable(to appear).
- Zvonimir Janko and John G. Thompson, On finite simple groups whose Sylow $2$-subgroups have no normal elementary subgroups of order $8$, Math. Z. 113 (1970), 385β397. MR 283076, DOI 10.1007/BF01110509
- Anne R. MacWilliams, On $2$-groups with no normal abelian subgroups of rank $3$, and their occurrence as Sylow $2$-subgroups of finite simple groups, Trans. Amer. Math. Soc. 150 (1970), 345β408. MR 276324, DOI 10.1090/S0002-9947-1970-0276324-3
- John G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc. 74 (1968), 383β437. MR 230809, DOI 10.1090/S0002-9904-1968-11953-6
- George Glauberman, A characteristic subgroup of a $p$-stable group, Canadian J. Math. 20 (1968), 1101β1135. MR 230807, DOI 10.4153/CJM-1968-107-2
- George Glauberman, Central elements in core-free groups, J. Algebra 4 (1966), 403β420. MR 202822, DOI 10.1016/0021-8693(66)90030-5
- David M. Goldschmidt, Solvable signalizer functors on finite groups, J. Algebra 21 (1972), 137β148. MR 297861, DOI 10.1016/0021-8693(72)90040-3
- David M. Goldschmidt, $2$-signalizer functors on finite groups, J. Algebra 21 (1972), 321β340. MR 323904, DOI 10.1016/0021-8693(72)90027-0
- Daniel Gorenstein, On the centralizers of involutions in finite groups, J. Algebra 11 (1969), 243β277. MR 240188, DOI 10.1016/0021-8693(69)90056-8
- Daniel Gorenstein, The flatness of signalizer functors on finite groups, J. Algebra 13 (1969), 509β512. MR 251121, DOI 10.1016/0021-8693(69)90112-4
- Daniel Gorenstein, On finite simple groups of characteristic $2$ type, Inst. Hautes Γtudes Sci. Publ. Math. 36 (1969), 5β13. MR 260864 53. D. Gorenstein, Centralizers of involutions in simple groups, Lecture Notes, Oxford University Group Theory Conference (to appear).
- Daniel Gorenstein and John H. Walter, Centralizers of involutions in balanced groups, J. Algebra 20 (1972), 284β319. MR 292927, DOI 10.1016/0021-8693(72)90060-9
- J. L. Alperin, Richard Brauer, and Daniel Gorenstein, Finite groups with quasi-dihedral and wreathed Sylow $2$-subgroups, Trans. Amer. Math. Soc. 151 (1970), 1β261. MR 284499, DOI 10.1090/S0002-9947-1970-0284499-5
- J. L. Alperin, Richard Brauer, and Daniel Gorenstein, Finite simple groups of $2$-rank two, Scripta Math. 29 (1973), no.Β 3-4, 191β214. MR 401902
- Richard Brauer, Some applications of the theory of blocks of characters of finite groups. II, J. Algebra 1 (1964), 307β334. MR 174636, DOI 10.1016/0021-8693(64)90011-0
- Richard Brauer and Michio Suzuki, On finite groups of even order whose $2$-Sylow group is a quaternion group, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1757β1759. MR 109846, DOI 10.1073/pnas.45.12.1757
- Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775β1029. MR 166261
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
Additional Information
- Journal: Bull. Amer. Math. Soc. 77 (1971), 829-862
- MSC (1970): Primary 20D05, 20-02; Secondary 20D20
- DOI: https://doi.org/10.1090/S0002-9904-1971-12794-5
- MathSciNet review: 0306301