Equation 677 Database

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Magma 669d00c69dce…

magma 669d00c69dce
Size
595
Isomorphism class hash
669d00c69dcecc48549874e8d7435f11a4d3ab92b8097f6313081be87327c214
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
2026-10-06 14:30:09
Display reorder
302,300,301,305,303,304,509,508,505,504,506,507,453,452,454,455,450,451,442,441,443,438,439,440,447,446,448,449,444,445,555,594,593,592,591,69,71,70,67,66,68,46,45,47,44,42,43,51,53,52,49,50,48,28,27,29,26,24,25,32,31,30,34,35,33,15,17,16,14,12,13,22,21,23,18,19,20,75,77,76,72,74,73,59,58,57,56,54,55,40,39,41,38,36,37,458,457,459,460,461,456,327,326,328,329,324,325,314,313,315,316,317,312,361,360,362,363,364,365,321,320,322,323,318,319,467,466,462,463,464,465,538,537,536,517,518,533,535,516,510,557,563,561,589,577,574,584,276,277,278,280,281,279,106,105,107,104,102,103,111,113,112,109,110,108,86,85,84,87,88,89,82,81,83,78,79,80,2,0,1,4,5,3,284,282,283,286,287,285,93,95,94,91,92,90,119,118,117,116,114,115,100,99,101,98,96,97,430,429,431,427,426,428,357,356,358,359,354,355,344,343,345,346,347,342,337,336,338,339,340,341,351,350,352,353,348,349,478,477,479,474,475,476,550,539,540,520,521,515,551,519,511,556,562,568,587,579,572,581,61,60,62,64,65,63,134,133,132,135,136,137,139,138,140,143,141,142,270,271,272,275,273,274,125,124,123,121,122,120,266,264,265,268,269,267,128,127,126,130,131,129,152,151,150,153,154,155,144,146,145,147,148,149,156,158,157,160,161,159,468,473,469,470,471,472,368,367,369,370,371,366,375,374,376,377,372,373,331,330,332,333,334,335,382,381,383,378,379,380,482,481,483,484,485,480,549,548,541,522,531,530,547,523,512,559,567,566,586,576,571,582,290,288,289,293,291,292,240,242,241,244,245,243,248,247,246,249,250,251,238,237,239,236,234,235,228,230,229,233,231,232,8,7,6,10,11,9,298,297,299,295,294,296,222,224,223,226,227,225,253,252,254,256,257,255,219,221,220,217,218,216,432,437,433,434,435,436,413,412,408,409,410,411,407,406,402,403,404,405,400,399,401,396,397,398,420,421,422,423,424,425,503,502,498,499,500,501,553,552,546,527,528,534,554,526,514,558,564,569,590,580,575,585,215,214,213,212,210,211,165,167,166,163,164,162,173,172,171,168,169,170,192,194,193,196,197,195,202,201,203,198,199,200,207,209,208,206,204,205,186,188,187,191,189,190,183,185,184,181,182,180,178,177,179,175,176,174,259,258,260,263,261,262,492,497,493,494,495,496,385,384,386,387,388,389,306,307,308,309,310,311,392,391,393,394,395,390,414,419,415,416,417,418,486,491,487,488,489,490,545,543,542,524,525,532,544,529,513,560,570,565,588,578,573,583 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 {36, 66} (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 2026-10-06 14:30:10 · history