Equation 677 Database

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Magma 9a2860a75f71…

magma 9a2860a75f71
Size
705
Isomorphism class hash
9a2860a75f71c563857a1f91f5d2cc470eec9dbd8765bf6e506222444292a713
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 21:11:14
Display reorder
704,493,224,509,528,494,507,529,222,492,223,508,530,505,496,227,531,506,497,225,532,504,495,226,533,515,499,534,219,513,500,535,220,514,498,536,221,502,511,537,218,503,512,538,216,501,510,539,217,518,516,517,521,519,520,524,522,526,527,525,523,660,662,661,663,158,382,127,153,156,128,154,383,157,381,126,155,130,161,378,152,131,159,379,150,129,160,380,151,125,164,144,373,123,162,145,374,124,163,146,372,167,121,147,376,165,122,148,377,166,120,149,375,133,134,132,136,137,135,139,140,141,142,143,138,691,688,690,689,553,15,568,592,554,569,593,16,552,17,567,591,564,556,14,588,565,557,12,589,566,555,13,590,574,559,598,21,575,560,599,22,573,558,597,23,562,570,594,20,563,571,595,18,561,572,596,19,579,580,581,578,576,577,585,586,583,584,582,587,671,668,670,669,395,10,402,429,393,403,430,11,394,9,404,431,405,391,6,428,406,392,7,426,407,390,8,427,400,386,420,0,401,384,421,2,399,385,422,1,389,396,423,4,387,397,424,5,388,398,425,3,413,411,412,409,410,408,419,417,414,415,416,418,678,676,679,677,261,103,266,243,262,264,244,104,263,102,265,245,269,260,106,242,267,258,107,240,268,259,105,241,272,252,249,101,270,253,250,99,271,254,251,100,255,275,248,97,256,273,246,98,257,274,247,96,237,238,239,236,234,235,228,229,233,231,232,230,666,664,667,665,656,659,657,658,648,649,650,651,652,655,653,654,641,640,643,642,645,644,647,646,637,636,639,638,621,620,622,623,613,612,614,615,617,616,618,619,633,632,634,635,624,625,626,627,629,628,630,631,540,541,542,543,544,545,546,547,551,549,550,548,692,695,693,694,79,38,89,68,80,87,66,36,78,37,88,67,85,82,41,71,86,83,39,69,84,81,40,70,95,77,63,44,93,75,64,42,94,76,65,43,73,91,62,47,74,92,60,45,72,90,61,46,58,59,57,54,55,56,49,50,51,52,53,48,700,703,701,702,309,115,312,291,310,313,292,116,311,114,314,293,315,308,118,290,316,306,119,288,317,307,117,289,318,300,297,113,319,301,298,111,320,302,299,112,303,321,296,109,304,322,294,110,305,323,295,108,276,277,278,279,280,281,282,283,287,285,286,284,696,699,697,698,168,490,189,215,169,190,213,491,170,489,191,214,188,171,486,211,186,172,487,212,187,173,488,210,180,174,206,481,181,175,204,482,182,176,205,480,177,183,209,484,178,184,207,485,179,185,208,483,197,195,196,193,194,192,203,201,198,199,200,202,675,672,674,673,326,29,343,364,324,344,365,27,325,28,342,363,346,329,25,360,347,327,26,361,345,328,24,362,341,332,370,35,339,330,371,33,340,331,369,34,335,337,366,31,333,338,367,32,334,336,368,30,348,349,350,351,352,353,354,355,359,357,358,356,680,681,683,682,464,609,475,446,462,476,444,610,463,611,474,445,478,467,608,449,479,465,606,447,477,466,607,448,473,459,452,600,471,460,450,601,472,461,451,602,458,469,455,603,456,470,453,604,457,468,454,605,443,441,442,439,440,438,434,432,436,437,435,433,684,686,685,687 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#dc3952d3945a57ff89efbf9c91902a27e7bb606727f60175866197715516bbc5, 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 21:11:15 · history