Equation 677 Database

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Magma 974de3a504c9…

magma 974de3a504c9
Size
705
Isomorphism class hash
974de3a504c9feaaf37583ae5351d4fb75b0745bf95435355519ff1bee98d764
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 18:08:28
Display reorder
704,501,85,471,490,502,86,491,472,503,84,489,473,500,88,470,486,498,89,468,487,499,87,488,469,91,492,477,481,92,493,482,478,90,494,480,479,94,495,476,484,95,496,485,474,93,497,483,475,505,506,504,508,509,507,511,512,513,514,515,510,661,662,660,663,319,30,341,358,320,31,359,339,318,32,357,340,322,33,337,354,323,34,338,355,321,35,356,336,28,317,347,349,29,315,350,345,27,316,348,346,24,313,343,352,25,314,353,344,26,312,351,342,327,328,329,326,324,325,333,334,331,332,330,335,690,688,691,689,529,97,559,518,530,98,516,560,528,96,517,558,532,100,562,521,533,101,563,519,531,99,520,561,103,535,557,524,104,536,522,555,102,534,523,556,106,538,553,527,107,539,525,554,105,537,526,552,548,546,547,551,549,550,543,544,541,542,540,545,670,668,671,669,398,37,383,384,396,38,385,381,397,36,386,382,401,40,379,387,399,41,380,388,400,39,389,378,43,404,374,390,44,402,391,372,42,403,392,373,46,407,377,393,47,405,394,375,45,406,395,376,371,369,370,367,368,366,362,360,364,365,363,361,679,676,678,677,195,58,175,184,196,59,185,176,197,57,183,174,194,54,178,180,192,55,179,181,193,56,182,177,49,201,173,190,50,202,191,171,48,203,189,172,52,200,169,186,53,198,187,170,51,199,188,168,214,215,213,210,211,212,205,206,207,208,209,204,667,664,666,665,659,657,656,658,650,648,651,649,655,653,654,652,643,641,640,642,647,645,644,646,639,636,638,637,621,623,620,622,613,615,614,612,617,619,618,616,633,635,632,634,624,627,626,625,629,631,630,628,82,83,81,78,79,80,73,74,75,76,77,72,693,695,692,694,135,161,116,124,136,159,125,114,137,160,123,115,134,157,119,120,132,158,117,121,133,156,122,118,167,141,111,130,165,142,131,112,166,143,129,113,163,140,110,126,164,138,127,108,162,139,128,109,155,153,154,151,152,150,146,144,148,149,147,145,701,703,700,702,252,11,238,242,253,9,240,239,254,10,241,237,255,7,234,245,256,8,235,243,257,6,244,236,2,258,229,248,1,259,246,230,0,260,247,228,5,261,232,251,3,262,249,233,4,263,250,231,225,226,227,224,222,223,216,217,221,219,220,218,697,699,696,698,466,60,437,453,467,61,454,435,465,62,455,436,462,63,433,452,463,64,434,450,464,65,451,432,66,457,443,444,67,458,445,441,68,456,446,442,69,460,439,447,70,461,448,440,71,459,449,438,423,424,425,422,420,421,429,430,427,428,426,431,674,672,675,673,266,19,296,303,264,20,304,294,265,18,305,295,269,22,299,302,267,23,297,300,268,21,301,298,17,272,291,309,15,270,310,292,16,271,311,293,13,275,290,308,14,273,306,288,12,274,307,289,282,283,284,285,286,287,280,281,278,276,277,279,683,681,680,682,579,408,609,567,580,409,568,610,581,410,569,611,578,411,608,566,576,412,606,564,577,413,565,607,414,585,600,573,415,586,574,601,416,587,575,602,417,584,603,572,418,582,570,604,419,583,571,605,598,599,597,594,595,596,589,590,591,592,593,588,685,686,684,687 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#65891b0f2ef20500afb660f1d25606412fdc1bf33a195bdba8e3c07ff4e9e9d9, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 18:08:29 · history