Equation 677 Database

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Magma 692463a6667a…

magma 692463a6667a
Size
381
Isomorphism class hash
692463a6667ab8312aec12e251eff656071d4b6d1bb779751dd9ec67515896f6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:25:30
Display reorder
380,147,142,122,127,132,137,17,22,27,2,7,12,37,42,47,52,57,32,262,267,242,247,252,257,304,305,301,300,302,303,77,82,87,62,67,72,217,222,227,232,237,212,97,102,107,112,117,92,187,192,197,202,207,182,157,167,152,172,177,162,284,294,279,298,274,289,366,352,359,376,333,360,349,336,371,344,148,143,123,128,133,138,18,23,28,3,8,13,38,43,48,53,58,33,263,268,243,248,253,258,329,324,325,326,327,328,78,83,88,63,68,73,218,223,228,233,238,213,98,103,108,113,118,93,188,193,198,203,208,183,158,168,153,173,178,163,280,290,276,299,271,285,369,335,356,379,342,362,351,350,374,334,145,141,121,126,131,136,16,21,26,1,6,11,36,41,46,50,55,31,261,265,240,245,250,255,313,314,315,316,317,312,75,81,86,60,65,70,216,221,225,230,235,211,96,101,106,110,115,91,186,191,195,200,205,181,156,165,151,170,175,160,283,293,278,297,273,288,367,346,358,377,343,364,332,347,372,330,146,140,120,125,130,135,15,20,25,0,5,10,35,40,45,51,56,30,260,266,241,246,251,256,319,320,321,322,323,318,76,80,85,61,66,71,215,220,226,231,236,210,95,100,105,111,116,90,185,190,196,201,206,180,155,166,150,171,176,161,281,291,275,296,272,286,368,348,357,378,331,361,337,338,373,341,149,144,124,129,134,139,19,24,29,4,9,14,39,44,49,54,59,34,264,269,244,249,254,259,310,311,306,307,308,309,79,84,89,64,69,74,219,224,229,234,239,214,99,104,109,114,119,94,189,194,199,204,209,184,159,169,154,174,179,164,282,292,277,295,270,287,365,339,355,375,345,363,354,353,370,340 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {75} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:25:31 · history