Equation 677 Database

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Magma 9aa0d747bd36…

magma 9aa0d747bd36
Size
705
Isomorphism class hash
9aa0d747bd36ade59b91bbb6d14c2c29e920fecae260e2a26dead2ffd8ae4023
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 20:00:27
Display reorder
660,401,400,399,396,397,398,406,407,405,402,403,404,274,275,273,270,271,272,265,266,264,268,269,267,335,333,334,331,332,330,326,324,325,329,327,328,64,65,63,60,61,62,70,71,69,66,67,68,260,258,259,263,261,262,255,256,257,254,252,253,670,679,682,689,362,361,360,364,365,363,367,368,366,370,371,369,151,152,150,154,155,153,149,147,148,145,146,144,563,561,562,559,560,558,554,552,553,557,555,556,186,187,188,189,190,191,184,185,183,180,181,182,16,17,15,12,13,14,22,23,21,18,19,20,662,664,666,675,518,517,516,520,521,519,523,524,522,526,527,525,458,456,457,461,459,460,464,462,463,467,465,466,582,583,584,585,586,587,580,581,579,576,577,578,477,478,479,476,474,475,468,469,470,471,472,473,453,454,455,452,450,451,444,445,446,447,448,449,673,678,683,690,323,322,321,318,319,320,313,314,312,316,317,315,385,386,384,388,389,387,391,392,390,394,395,393,46,47,45,42,43,44,37,38,36,40,41,39,92,90,91,95,93,94,87,88,89,86,84,85,24,25,26,27,28,29,30,31,32,33,34,35,695,702,701,704,240,242,241,245,243,244,248,246,247,251,249,250,487,488,486,490,491,489,485,483,484,481,482,480,120,121,122,123,124,125,126,127,128,129,130,131,597,598,599,596,594,595,588,589,590,591,592,593,538,539,537,534,535,536,529,530,528,532,533,531,685,692,693,698,658,657,659,656,654,655,648,649,650,651,652,653,628,629,627,624,625,626,634,635,633,630,631,632,620,618,619,623,621,622,615,616,617,614,612,613,600,601,602,603,604,605,606,607,608,609,610,611,637,638,636,640,641,639,643,644,642,646,647,645,663,669,668,674,9,11,10,7,8,6,2,1,0,5,3,4,511,512,510,514,515,513,509,507,508,505,506,504,199,200,198,202,203,201,197,195,196,193,194,192,569,567,568,565,566,564,575,573,574,571,572,570,503,501,502,499,500,498,494,492,493,497,495,496,684,691,694,697,132,134,133,137,135,136,140,138,139,143,141,142,171,172,173,170,168,169,177,178,179,176,174,175,348,349,350,351,352,353,354,355,356,357,358,359,542,540,541,545,543,544,548,546,547,551,549,550,211,212,210,214,215,213,209,207,208,205,206,204,672,686,681,688,431,430,429,426,427,428,421,422,420,424,425,423,440,438,439,443,441,442,435,436,437,434,432,433,59,57,58,55,56,54,50,48,49,53,51,52,296,294,295,299,297,298,291,292,293,290,288,289,228,229,230,231,232,233,234,235,236,237,238,239,696,699,700,703,113,112,111,108,109,110,118,119,117,114,115,116,300,301,302,303,304,305,306,307,308,309,310,311,376,377,375,372,373,374,382,383,381,378,379,380,157,158,156,160,161,159,163,164,162,166,167,165,99,100,101,98,96,97,105,106,107,104,102,103,661,665,667,676,76,75,77,74,72,73,81,82,83,80,78,79,347,345,346,343,344,342,338,336,337,341,339,340,218,216,217,221,219,220,224,222,223,227,225,226,285,286,287,284,282,283,276,277,278,279,280,281,410,408,409,413,411,412,416,414,415,419,417,418,671,677,680,687 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {62} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 20:00:28 · history