Equation 677 Database

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Magma b92bf8d52824…

magma b92bf8d52824
Size
705
Isomorphism class hash
b92bf8d528249a029e0cd6c5e222c4ad9e16725cee6c69d95cf158aff9ff5bbd
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 15:15:36
Display reorder
660,399,199,423,258,47,400,200,424,256,48,201,257,398,422,46,402,198,426,261,50,403,196,427,259,51,401,197,425,260,49,205,397,421,264,45,206,395,419,262,43,207,396,420,263,44,204,393,417,267,41,202,394,418,265,42,203,392,416,266,40,662,663,671,666,507,102,385,459,138,508,100,383,460,136,101,458,506,384,137,510,105,381,462,141,511,103,382,463,139,509,104,380,461,140,108,505,391,457,144,106,503,389,455,142,107,504,390,456,143,111,501,387,453,147,109,502,388,454,145,110,500,386,452,146,688,690,685,687,623,170,567,224,285,624,171,568,225,283,169,223,622,566,284,626,166,570,220,281,627,167,571,221,282,625,168,569,222,280,161,621,565,230,291,162,619,563,231,289,160,620,564,229,290,164,617,561,226,287,165,618,562,227,288,163,616,560,228,286,672,667,668,664,321,58,296,555,306,319,59,297,556,304,60,554,320,295,305,317,61,292,558,309,318,62,293,559,307,316,63,294,557,308,56,327,302,553,312,57,325,303,551,310,55,326,301,552,311,52,323,298,549,315,53,324,299,550,313,54,322,300,548,314,677,674,683,680,587,333,2,65,599,588,331,1,66,600,332,64,586,0,598,590,329,5,68,602,591,330,3,69,603,589,328,4,67,601,339,585,8,71,597,337,583,6,72,595,338,584,7,70,596,335,581,11,74,593,336,582,9,75,594,334,580,10,73,592,669,661,670,665,531,212,276,152,447,532,213,274,153,448,211,151,530,275,446,534,208,279,148,450,535,209,277,149,451,533,210,278,150,449,218,529,271,158,445,219,527,272,159,443,217,528,273,157,444,214,525,270,154,441,215,526,268,155,442,216,524,269,156,440,696,698,694,693,12,29,579,635,20,646,30,647,644,645,28,634,13,578,21,653,32,652,654,655,657,33,656,658,659,648,31,649,650,651,35,14,573,629,25,36,15,574,630,26,34,16,572,628,27,38,17,576,632,24,39,18,577,633,22,37,19,575,631,23,702,701,704,703,349,122,471,83,341,636,123,472,84,637,121,82,348,470,340,640,118,474,86,641,642,119,475,87,643,639,120,473,85,638,113,355,469,81,344,114,353,467,79,342,112,354,468,80,343,116,351,465,77,347,117,352,466,78,345,115,350,464,76,346,699,695,700,697,495,194,611,414,543,496,195,612,415,544,193,413,494,610,542,498,190,614,410,546,499,191,615,411,547,497,192,613,412,545,185,493,609,405,541,186,491,607,406,539,184,492,608,404,540,188,489,605,408,537,189,490,606,409,538,187,488,604,407,536,676,682,678,673,368,97,483,125,360,369,98,484,126,361,99,124,370,482,359,371,96,486,128,356,372,94,487,129,357,373,95,485,127,358,88,374,481,131,366,89,375,479,132,367,90,376,480,130,365,91,377,477,134,362,92,378,478,135,363,93,379,476,133,364,681,675,684,679,519,180,244,236,435,520,178,245,237,436,179,235,518,246,434,522,183,247,232,438,523,181,248,233,439,521,182,249,234,437,175,517,250,242,433,176,515,251,243,431,177,516,252,241,432,174,513,253,238,429,172,514,254,239,430,173,512,255,240,428,689,691,686,692 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#0d8cdfdeb3c53efefcd572d9bf5ad220efd26f91f8a2b4cfd66b53f1dccf6eeb, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 15:15:37 · history