Equation 677 Database

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Magma e103eddb4d09…

magma e103eddb4d09
Size
705
Isomorphism class hash
e103eddb4d09b3b1333a642270357773a4fa7401acb08007ba759529fa69733f
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 19:48:10
Display reorder
660,119,408,549,573,384,117,409,550,574,385,551,118,575,386,410,407,115,548,572,383,405,546,116,570,381,406,114,547,571,382,125,540,399,564,375,123,541,400,565,376,124,542,401,566,377,543,121,402,567,378,544,122,403,568,379,545,120,404,569,380,687,676,685,678,156,344,360,324,308,157,342,361,325,306,362,158,326,307,343,340,155,359,323,304,341,357,153,321,305,339,154,358,322,303,162,351,350,315,314,163,352,348,316,312,164,353,349,317,313,354,161,346,318,310,355,159,347,319,311,356,160,345,320,309,663,661,665,669,91,474,537,513,238,92,475,538,514,239,539,90,515,237,476,473,94,536,512,241,471,534,95,510,242,472,93,535,511,240,97,528,465,504,236,98,529,466,505,234,96,530,467,506,235,531,100,468,507,232,532,101,469,508,233,533,99,470,509,231,682,674,683,681,54,640,637,636,641,55,648,645,644,649,652,56,653,657,656,632,57,628,629,633,616,613,58,612,617,624,59,620,621,625,52,88,216,85,447,53,89,217,86,448,51,87,218,84,449,588,48,591,592,593,596,49,600,597,601,606,50,608,605,609,704,697,703,698,181,290,300,486,459,182,288,301,487,460,302,180,488,461,289,286,184,299,485,458,287,297,185,483,456,285,183,298,484,457,187,291,281,477,450,188,292,279,478,451,186,293,280,479,452,294,190,284,480,453,295,191,282,481,454,296,189,283,482,455,692,691,690,689,60,265,276,254,525,61,266,277,252,526,278,62,253,527,264,261,63,275,250,524,262,273,64,251,522,263,65,274,249,523,66,267,256,245,516,67,268,257,243,517,68,269,255,244,518,270,69,259,248,519,271,70,260,246,520,272,71,258,247,521,671,668,662,670,83,144,198,9,205,81,145,199,10,206,200,82,11,204,146,147,79,201,8,208,148,202,80,6,209,149,78,203,7,207,74,196,142,1,211,72,197,143,0,212,73,195,141,2,210,192,77,138,3,214,193,75,139,4,215,194,76,140,5,213,695,694,696,693,102,561,396,420,585,103,562,397,421,586,398,104,422,587,563,560,105,395,419,584,558,393,106,417,582,559,107,394,418,583,108,387,552,411,576,109,388,553,412,577,110,389,554,413,578,390,111,555,414,579,391,112,556,415,580,392,113,557,416,581,679,688,677,686,19,643,642,638,639,20,651,650,646,647,658,18,654,655,659,635,22,634,630,631,619,618,23,614,615,627,21,626,622,623,17,464,491,151,179,15,462,489,152,177,16,463,490,150,178,594,13,595,589,590,602,14,603,598,599,610,12,611,604,607,702,700,699,701,134,225,444,501,172,132,226,445,502,173,446,133,503,171,227,228,137,443,500,175,229,441,135,498,176,230,136,442,499,174,129,435,223,492,170,130,436,224,493,168,131,437,222,494,169,438,128,219,495,166,439,126,220,496,167,440,127,221,497,165,667,672,666,664,40,372,432,28,336,41,373,433,29,337,434,39,27,338,374,371,36,431,24,335,369,429,37,25,333,370,38,430,26,334,46,423,363,34,327,47,424,364,35,328,45,425,365,33,329,426,42,366,30,330,427,43,367,31,331,428,44,368,32,332,684,673,680,675 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#aa12d1af20c50a7f712e8df2ac0f984d22557fb7db3e49cc75c20296525d3597, 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 19:48:10 · history