Equation 677 Database

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Magma 9d1a150dda7b…

magma 9d1a150dda7b
Size
705
Isomorphism class hash
9d1a150dda7b1bb0c6a747482490a88faa640560e833db4312449ba4f711152e
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 16:50:57
Display reorder
660,550,273,500,476,352,474,274,548,498,350,272,475,549,499,351,276,553,503,479,355,551,277,501,477,353,275,552,502,478,354,545,279,495,471,347,546,280,496,472,348,547,278,497,473,349,282,544,494,470,346,283,542,492,468,344,281,543,493,469,345,688,684,674,682,180,71,30,376,514,374,69,181,31,512,70,375,179,32,513,67,176,33,379,517,177,68,34,377,515,66,178,35,378,516,186,62,28,371,509,187,60,29,372,510,185,61,27,373,511,65,182,24,370,508,63,183,25,368,506,64,184,26,369,507,668,672,669,663,204,138,388,526,199,524,136,205,386,197,137,525,203,387,198,141,200,391,529,195,201,139,389,527,196,140,202,390,528,194,210,144,383,521,190,211,142,384,522,188,209,143,385,523,189,147,206,382,520,193,145,207,380,518,191,146,208,381,519,192,681,676,678,686,631,101,628,633,630,617,99,615,613,614,100,625,623,621,622,97,655,653,657,654,639,98,637,641,638,96,647,645,649,646,591,107,589,593,590,599,105,596,601,598,607,106,604,609,606,103,582,580,585,584,104,162,120,466,161,102,163,121,467,160,698,700,703,704,436,287,412,424,227,422,288,434,410,228,289,423,435,411,229,286,439,415,427,226,437,284,413,425,224,285,438,414,426,225,431,293,407,419,233,432,294,408,420,234,433,295,409,421,235,292,430,406,418,232,290,428,404,416,230,291,429,405,417,231,692,690,689,691,113,159,221,488,462,486,157,111,222,460,158,487,112,223,461,155,109,220,491,465,110,156,218,489,463,154,108,219,490,464,119,150,212,483,457,117,148,213,484,458,118,149,214,485,459,153,115,215,482,456,151,116,216,480,454,152,114,217,481,455,661,670,666,667,573,81,572,254,330,255,82,568,569,331,83,256,571,570,329,80,579,578,257,326,574,78,575,258,327,79,577,576,259,328,562,72,563,252,321,564,73,565,253,322,567,74,566,251,320,75,561,560,248,324,76,556,557,249,325,77,559,558,250,323,696,695,693,694,46,89,342,538,268,536,87,47,343,266,88,537,45,341,267,85,42,338,541,271,43,86,339,539,269,84,44,340,540,270,37,95,333,533,263,38,93,334,534,264,36,94,332,535,265,91,40,336,532,262,92,41,337,530,260,90,39,335,531,261,680,679,677,687,632,7,635,634,629,618,8,616,619,612,6,626,624,627,620,10,656,659,658,652,640,11,643,642,636,9,648,651,650,644,592,5,595,594,588,600,3,603,602,597,608,4,611,610,605,0,586,587,583,581,2,453,554,504,122,1,452,555,505,123,697,702,701,699,364,48,167,400,132,398,49,362,168,130,50,399,363,169,131,51,367,166,403,135,365,52,164,401,133,53,366,165,402,134,359,54,173,395,127,360,55,174,396,128,361,56,175,397,129,57,358,172,394,126,58,356,170,392,124,59,357,171,393,125,662,665,671,664,317,16,240,448,302,446,17,318,241,303,15,447,319,239,304,12,316,236,451,305,314,13,237,449,306,14,315,238,450,307,308,22,246,443,300,309,23,247,444,301,310,21,245,445,299,18,311,242,442,296,19,312,243,440,297,20,313,244,441,298,683,673,685,675 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#40ac4fa024666665509cd5e942b6a945fc35db692a456c0e176de1fe3e839a09, M = {60} 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 16:50:58 · history