SUMMARY / RELATED TOPICS

P-stable group

In finite group theory, a p-stable group for an odd prime p is a finite group satisfying a technical condition introduced by Gorenstein and Walter in order to extend Thompson's uniqueness results in the odd order theorem to groups with dihedral Sylow 2-subgroups. There are several equivalent definitions of a p-stable group. First definition. We give definition of a p-stable group in two parts; the definition used here comes from. 1. Let p be an odd prime and G be a finite group with a nontrivial p-core O p. G is p-stable if it satisfies the following condition: Let P be an arbitrary p-subgroup of G such that O p ′ is a normal subgroup of G. Suppose that x ∈ N G and x ¯ is the coset of C G containing x. If = 1 x ¯ ∈ O n. Now, define M p as the set of all p-subgroups of G maximal with respect to the property that O p ≠ 1. 2. Let G be a finite group and p an odd prime. G is called p-stable if every element of M p is p-stable by definition 1. Second definition. Let p be an odd prime and H a finite group.

H is p-stable if F ∗ = O p and, whenever P is a normal p-subgroup of H and g ∈ H with = 1 g C H ∈ O p. If p is an odd prime and G is a finite group such that SL2 is not involved in G G is p-stable. If furthermore G contains a normal p-subgroup P such that C G ⩽ P Z is a characteristic subgroup of G, where J 0 is the subgroup introduced by John Thompson in. P-stability is used as one of the conditions in Glauberman's ZJ theorem. Quadratic pair p-constrained group p-solvable group Glauberman, George, "A characteristic subgroup of a p-stable group", Canadian Journal of Mathematics, 20: 1101–1135, doi:10.4153/cjm-1968-107-2, ISSN 0008-414X, MR 0230807 Thompson, John G. "A replacement theorem for p-groups and a conjecture", Journal of Algebra, 13: 149–151, doi:10.1016/0021-869390068-4, ISSN 0021-8693, MR 0245683 Gorenstein, D.. "On the maximal subgroups of finite simple groups", Journal of Algebra, 1: 168–213, doi:10.1016/0021-869390032-8, ISSN 0021-8693, MR 0172917 Gorenstein, D.. "The characterization of finite groups with dihedral Sylow 2-subgroups.

I", Journal of Algebra, 2: 85–151, doi:10.1016/0021-869390027-X, ISSN 0021-8693, MR 0177032 Gorenstein, D.. "The characterization of finite groups with dihedral Sylow 2-subgroups. II", Journal of Algebra, 2: 218–270, doi:10.1016/0021-869390019-0, ISSN 0021-8693, MR 0177032 Gorenstein, D.. "The characterization of finite groups with dihedral Sylow 2-subgroups. III", Journal of Algebra, 2: 354–393, doi:10.1016/0021-869390015-3, ISSN 0021-8693, MR 0190220 Gorenstein, D. "The classification of finite simple groups. I. Simple groups and local analysis", American Mathematical Society. Bulletin. New Series, 1: 43–199, doi:10.1090/S0273-0979-1979-14551-8, ISSN 0002-9904, MR 0513750 Gorenstein, D. Finite groups, New York: Chelsea Publishing Co. ISBN 978-0-8284-0301-6, MR 0569209

Wrestling at the 1980 Summer Olympics – Men's Greco-Roman 57 kg

The Men's Greco-Roman 57 kg at the 1980 Summer Olympics as part of the wrestling program were held at the Athletics Fieldhouse, Central Sports Club of the Army. The competition used a form of negative points tournament, with negative points given for any result short of a fall. Accumulation of 6 negative points eliminated the loser wrestler; when only three wrestlers remain, a special final round is used to determine the order of the medals. LegendTF — Won by Fall IN — Won by Opponent Injury DQ — Won by Passivity D1 — Won by Passivity, the winner is passive too D2 — Both wrestlers lost by Passivity FF — Won by Forfeit DNA — Did not appear TPP — Total penalty points MPP — Match penalty pointsPenalties0 — Won by Fall, Technical Superiority, Passivity and Forfeit 0.5 — Won by Points, 8-11 points difference 1 — Won by Points, 1-7 points difference 2 — Won by Passivity, the winner is passive too 3 — Lost by Points, 1-7 points difference 3.5 — Lost by Points, 8-11 points difference 4 — Lost by Fall, Technical Superiority, Passivity and Forfeit Results from the preliminary round are carried forward into the final.

Shamil Serikov Józef Lipień Benni Ljungbeck Mihai Boţilă Antonino Caltabiano Josef Krysta Gyula Molnár Georgi Donev Official Report