Equation 677 Database

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Magma 26468387ebc3…

magma 26468387ebc3
Size
705
Isomorphism class hash
26468387ebc33bf1a23d61ee36555209f4a8376d8ed3d434f12a70194016f5f9
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 15:32:24
Display reorder
660,490,0,321,436,105,322,2,437,491,106,1,489,323,435,107,320,4,432,486,104,5,318,433,487,102,319,3,434,488,103,312,7,442,496,111,313,8,443,497,112,314,6,441,495,113,10,315,438,492,110,11,316,439,493,108,9,317,440,494,109,683,678,676,686,412,125,99,466,60,100,123,467,413,61,124,411,101,465,62,98,121,462,408,63,122,96,463,409,64,97,120,464,410,65,90,116,472,418,58,91,114,473,419,59,92,115,471,417,57,119,93,468,414,54,117,94,469,415,55,118,95,470,416,56,663,664,666,667,400,532,19,454,39,20,533,455,401,40,531,399,18,453,41,22,528,450,396,38,529,23,451,397,36,21,530,452,398,37,17,538,460,406,30,15,539,461,407,31,16,537,459,405,32,534,13,456,402,33,535,14,457,403,34,536,12,458,404,35,680,675,677,679,448,526,129,178,246,130,527,179,449,247,525,447,131,177,248,128,522,174,444,249,523,126,175,445,250,127,524,176,446,251,135,649,648,646,645,136,657,656,654,653,137,641,640,638,637,614,134,613,617,616,625,132,624,622,620,633,133,632,630,628,703,697,704,700,364,502,327,478,267,328,503,479,365,268,501,363,329,477,269,326,498,474,360,266,499,324,475,361,264,325,500,476,362,265,333,508,484,370,273,334,509,485,371,274,335,507,483,369,275,504,332,480,366,272,505,330,481,367,270,506,331,482,368,271,689,691,693,694,514,75,195,388,167,196,76,389,515,165,77,513,197,387,166,194,74,384,510,163,72,192,385,511,164,193,73,386,512,162,201,66,394,520,173,202,67,395,521,171,203,68,393,519,172,69,200,390,516,169,70,198,391,517,170,71,199,392,518,168,668,669,662,661,376,340,226,291,89,227,341,292,377,87,339,375,225,293,88,222,336,290,372,85,337,223,288,373,86,224,338,289,374,84,217,346,297,382,80,218,347,298,383,78,216,345,299,381,79,342,220,296,378,83,343,221,294,379,81,344,219,295,380,82,695,692,696,690,604,586,311,352,568,309,587,353,605,569,585,603,310,351,567,307,582,348,600,564,583,308,349,601,565,306,584,350,602,566,302,592,358,610,574,300,593,359,611,575,301,591,357,609,573,588,305,354,606,570,589,303,355,607,571,590,304,356,608,572,682,688,673,685,580,241,239,598,26,237,242,599,581,24,240,579,238,597,25,235,244,594,576,29,245,236,595,577,27,234,243,596,578,28,230,644,651,650,647,228,652,659,658,655,229,636,643,642,639,618,233,619,615,612,621,231,627,626,623,629,232,635,634,631,698,701,702,699,252,544,53,142,424,51,545,143,253,425,543,254,52,141,423,49,540,138,255,420,541,50,139,256,421,48,542,140,257,422,44,550,148,258,430,42,551,149,259,431,43,549,147,260,429,546,47,144,261,426,547,45,145,262,427,548,46,146,263,428,665,672,671,670,186,556,153,279,215,154,557,280,187,213,555,188,155,281,214,152,552,278,189,211,553,150,276,190,212,151,554,277,191,210,159,562,285,184,206,160,563,286,185,204,161,561,287,183,205,558,158,284,180,209,559,156,282,181,207,560,157,283,182,208,674,687,684,681 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#1de75750e9587644a990145f0b96f270fc04381fd8036a009d6bb6ea07359c52, 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 15:32:25 · history