Equation 677 Database

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Magma 54c07c46d0ea…

magma 54c07c46d0ea
Size
705
Isomorphism class hash
54c07c46d0eac18981a4a4040ad7e28a0ce2ba63da58c3a3042c68d969bb0a01
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 19:48:32
Display reorder
660,346,35,604,594,13,347,33,605,595,14,345,34,603,596,12,349,31,600,597,16,350,32,601,598,17,348,30,602,599,15,26,352,610,592,19,24,353,611,593,20,351,25,609,591,18,355,29,606,588,22,356,27,607,589,23,354,28,608,590,21,687,688,686,685,261,410,387,428,396,262,408,388,426,397,263,409,389,427,398,264,406,390,424,395,265,407,391,425,393,266,405,392,423,394,416,267,385,419,402,414,268,386,417,403,269,415,384,418,404,270,412,381,422,401,271,413,382,420,399,272,411,383,421,400,703,704,701,702,340,586,557,543,575,341,587,555,544,573,339,585,556,545,574,343,582,553,542,571,344,583,554,540,572,342,584,552,541,570,577,338,563,549,566,578,336,561,550,564,337,576,562,551,565,334,580,559,548,569,335,581,560,546,567,333,579,558,547,568,671,672,670,669,430,206,183,223,192,431,204,184,224,193,429,205,185,222,194,433,202,186,219,191,434,203,187,220,189,432,201,188,221,190,212,436,181,214,198,210,437,182,215,199,435,211,180,213,200,439,208,177,217,197,440,209,178,218,195,438,207,179,216,196,679,680,678,677,47,234,258,242,447,45,235,259,240,448,46,236,260,241,449,43,233,257,238,450,44,231,255,239,451,42,232,256,237,452,225,38,249,248,445,226,36,250,246,446,37,227,251,247,444,41,228,252,244,441,39,229,253,245,442,40,230,254,243,443,692,691,690,689,311,71,94,83,507,309,69,95,81,508,310,70,93,82,509,314,67,90,79,510,312,68,91,80,511,313,66,92,78,512,62,317,85,74,505,60,315,86,72,506,316,61,84,73,504,320,65,88,77,501,318,63,89,75,502,319,64,87,76,503,699,700,698,697,167,134,163,152,120,165,132,164,150,121,166,133,162,151,122,170,130,159,148,119,168,131,160,149,117,169,129,161,147,118,140,173,154,143,126,138,171,155,141,127,172,139,153,142,128,176,136,157,146,125,174,137,158,144,123,175,135,156,145,124,663,664,662,661,359,638,618,9,628,357,636,619,10,629,358,637,620,11,627,362,641,621,8,624,360,639,622,6,625,361,640,623,7,626,644,365,616,1,634,642,363,617,0,635,364,643,615,2,633,368,647,612,3,630,366,645,613,4,631,367,646,614,5,632,682,683,684,681,331,96,523,519,531,332,97,524,520,532,330,98,522,521,533,327,657,658,656,659,328,648,650,649,651,329,652,654,653,655,102,322,529,517,537,103,323,530,518,538,321,104,528,516,539,325,101,525,513,536,326,99,526,514,534,324,100,527,515,535,695,696,693,694,55,493,466,455,486,56,494,467,453,487,54,492,465,454,488,58,489,469,458,485,59,490,470,456,483,57,491,468,457,484,499,53,472,461,477,500,51,473,459,478,52,498,471,460,479,49,495,475,464,480,50,496,476,462,481,48,497,474,463,482,667,668,665,666,112,375,290,279,308,113,376,288,280,306,111,377,289,281,307,115,378,286,282,304,116,379,287,283,305,114,380,285,284,303,373,110,296,277,299,374,108,294,278,297,109,372,295,276,298,106,369,292,273,302,107,370,293,274,300,105,371,291,275,301,675,676,673,674 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#ad2693ca9f316a407649b357541de7a5de95f31142bb6f4854bfa44084f1f633, M = {60} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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 19:48:33 · history