Equation 677 Database

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Magma 26ab990bdb2a…

magma 26ab990bdb2a
Size
705
Isomorphism class hash
26ab990bdb2a325568dfb3b796a852ff1959c630fac74d4da7c4be25d857e6a7
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 15:57:50
Display reorder
660,203,514,504,509,508,201,534,524,529,528,202,494,484,489,488,434,199,425,429,428,453,200,448,451,450,474,198,464,469,468,194,634,624,629,628,192,654,644,649,648,193,614,604,609,608,554,197,544,549,548,574,195,564,569,568,594,196,584,589,588,685,699,690,691,103,507,506,513,510,104,527,526,533,530,102,487,486,493,490,427,106,426,433,430,457,107,456,458,445,467,105,466,473,470,101,627,626,633,630,99,647,646,653,650,100,607,606,613,610,547,97,546,553,550,567,98,566,573,570,587,96,586,593,590,688,686,692,689,57,328,292,364,230,58,329,293,365,228,59,327,291,363,229,324,56,288,360,233,325,54,289,361,231,326,55,290,362,232,48,334,298,370,236,49,335,299,371,234,50,333,297,369,235,330,51,294,366,239,331,52,295,367,237,332,53,296,368,238,664,661,662,667,211,170,94,184,388,212,168,95,185,389,210,169,93,183,387,173,214,90,180,384,171,215,91,181,385,172,213,92,182,386,209,176,85,190,394,207,174,86,191,395,208,175,84,189,393,179,205,88,186,390,177,206,89,187,391,178,204,87,188,392,681,679,670,669,134,511,500,501,516,132,531,520,521,536,133,491,481,480,496,431,137,422,420,436,446,135,444,443,447,471,136,461,460,476,140,631,620,621,636,138,651,640,641,656,139,611,601,600,616,551,143,541,540,556,571,141,561,560,576,591,142,581,580,596,700,702,698,703,78,518,517,519,512,79,538,537,539,532,80,498,497,499,492,438,81,437,439,432,441,82,440,442,452,477,83,478,479,472,76,637,638,639,632,77,658,657,659,652,75,617,618,619,612,558,72,557,559,552,578,73,577,579,572,597,74,598,599,592,695,693,694,701,4,502,503,515,505,5,522,523,535,525,3,482,483,495,485,423,1,424,435,421,454,0,455,459,449,462,2,463,475,465,10,622,623,635,625,11,642,643,655,645,9,602,603,615,605,542,6,543,555,545,562,7,563,575,565,582,8,583,595,585,687,704,696,697,26,253,285,268,247,24,254,286,269,248,25,252,287,267,246,256,29,284,264,250,257,27,282,265,251,255,28,283,266,249,32,259,276,274,245,30,260,277,275,243,31,258,278,273,244,262,35,279,270,241,263,33,280,271,242,261,34,281,272,240,680,673,676,677,219,36,400,352,67,220,37,401,353,68,221,38,399,351,66,39,218,396,348,70,40,216,397,349,71,41,217,398,350,69,225,42,406,358,65,226,43,407,359,63,227,44,405,357,64,45,224,402,354,61,46,222,403,355,62,47,223,404,356,60,678,671,684,666,113,302,166,316,340,111,300,167,317,341,112,301,165,315,339,305,109,162,312,336,303,110,163,313,337,304,108,164,314,338,119,308,157,322,346,117,306,158,323,347,118,307,156,321,345,311,115,160,318,342,309,116,161,319,343,310,114,159,320,344,683,682,665,663,149,21,124,412,376,147,22,125,413,377,148,23,123,411,375,20,145,120,408,372,18,146,121,409,373,19,144,122,410,374,155,12,130,418,382,153,13,131,419,383,154,14,129,417,381,15,151,126,414,378,16,152,127,415,379,17,150,128,416,380,672,675,668,674 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#299bf89dcaadd64e33422b05a87b398de7449d556bda64ba0ca787ebaa3d1bcb, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 15:57:51 · history