Equation 677 Database

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Magma fb0d404207cc…

magma fb0d404207cc
Size
595
Isomorphism class hash
fb0d404207cc5cfafba50379d8bad7d888ad22d041b737bd58b82886155dd403
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 11:12:58
Display reorder
114,116,115,112,113,111,104,103,102,101,99,100,109,108,110,105,106,107,509,508,504,505,506,507,305,304,300,301,302,303,527,525,526,592,584,126,125,127,124,179,123,23,22,21,24,25,26,154,153,152,155,156,157,176,178,177,0,2,1,187,195,191,183,256,253,243,196,197,240,241,242,246,245,244,249,247,248,27,29,28,31,32,30,471,470,472,473,468,469,353,352,348,349,350,351,339,338,340,341,336,337,262,261,263,259,258,260,428,427,429,430,431,426,332,331,333,334,335,330,279,278,280,281,276,277,412,411,413,408,409,410,538,550,552,512,543,533,516,537,570,564,565,554,575,574,555,585,229,228,230,232,233,231,236,235,234,237,238,239,250,254,180,193,185,189,10,9,11,12,13,14,36,38,37,35,33,34,139,138,137,134,135,136,44,43,42,41,39,40,214,213,215,212,210,211,502,501,503,498,499,500,483,482,484,485,480,481,421,420,422,423,424,425,376,375,377,372,373,374,292,291,293,288,289,290,414,419,415,416,417,418,345,344,346,347,342,343,442,441,443,438,439,440,548,539,513,549,517,540,545,529,588,581,562,558,578,587,582,590,132,131,133,129,130,128,166,165,164,167,168,169,143,145,144,141,142,140,68,67,66,64,65,63,77,76,75,79,80,78,163,159,158,161,162,160,18,20,19,16,15,17,59,58,57,60,61,62,296,295,297,298,299,294,494,493,495,496,497,492,474,479,475,476,477,478,270,275,271,272,273,274,491,490,486,487,488,489,320,319,321,322,323,318,328,327,329,324,325,326,457,456,458,459,460,461,530,534,511,535,521,531,518,519,594,559,560,580,573,572,563,557,202,201,203,199,200,198,219,221,220,217,218,216,252,257,181,194,186,190,72,74,73,71,69,70,85,84,86,81,82,83,96,98,97,94,95,93,173,175,174,170,171,172,150,149,151,148,146,147,407,406,402,403,404,405,283,282,284,285,286,287,454,453,455,450,451,452,464,463,465,466,467,462,394,393,395,390,391,392,265,264,266,267,268,269,367,366,368,369,370,371,360,365,361,362,363,364,544,524,536,546,522,541,532,520,593,569,583,577,571,591,556,567,51,53,52,54,55,56,89,88,87,90,91,92,46,45,47,50,48,49,122,121,120,118,119,117,184,192,188,182,255,251,207,209,208,205,206,204,222,224,223,225,226,227,3,5,4,7,8,6,388,387,389,384,385,386,447,446,448,449,444,445,432,437,433,434,435,436,356,355,357,358,359,354,316,315,317,312,313,314,307,306,308,309,310,311,381,380,382,383,378,379,398,397,399,400,401,396,515,551,547,523,542,514,510,528,553,568,561,589,576,579,586,566 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = the submagma generated by {6, 36} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 11:13:00 · history