Equation 677 Database

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Magma d43b9afa60ac…

magma d43b9afa60ac
Size
705
Isomorphism class hash
d43b9afa60ace3797d99265c17dea382117642fd6e6a4c15decccee154eb8124
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 15:55:59
Display reorder
660,40,7,533,557,456,555,9,41,531,454,556,10,39,532,455,5,553,36,529,452,554,530,0,37,453,2,552,38,528,451,548,46,4,524,447,546,47,1,522,445,547,45,3,523,446,42,551,11,527,450,43,549,6,525,448,44,550,8,526,449,684,682,676,673,355,103,332,20,202,18,104,353,333,203,19,102,354,334,201,99,23,351,335,205,21,336,100,352,206,101,22,350,337,204,15,346,109,338,200,16,344,110,339,198,17,345,108,340,199,349,14,105,341,196,347,12,106,342,197,348,13,107,343,195,666,670,664,662,579,50,497,123,144,124,48,577,495,145,125,49,578,496,146,53,126,575,493,143,127,494,51,576,141,52,128,574,492,142,129,570,56,488,135,130,568,54,486,136,131,569,55,487,137,573,132,59,491,138,571,133,57,489,139,572,134,58,490,140,687,679,680,686,654,25,656,653,658,637,26,638,640,642,645,24,646,648,650,28,621,622,624,626,628,632,29,630,634,27,613,614,616,618,76,84,31,432,560,74,85,32,430,558,75,86,30,431,559,606,604,34,608,609,82,77,35,429,561,83,78,33,428,562,704,697,700,703,371,285,361,391,405,389,286,372,359,406,390,284,373,360,404,288,387,370,357,408,388,358,289,368,409,287,386,369,356,407,382,377,291,367,411,380,378,292,365,412,381,379,290,366,410,376,385,294,363,414,374,383,295,364,415,375,384,293,362,413,691,690,689,694,509,160,591,444,403,442,161,507,589,401,443,159,508,590,402,163,440,505,587,399,441,588,164,506,400,162,439,504,586,398,435,500,166,582,394,433,498,167,580,392,434,499,165,581,393,503,438,169,585,397,501,436,170,583,395,502,437,168,584,396,665,672,663,668,119,320,235,178,226,179,321,117,236,227,177,322,118,234,225,323,181,122,231,229,182,232,324,120,230,325,180,121,233,228,176,114,326,241,224,174,115,327,242,222,175,116,328,240,223,113,172,329,237,220,111,173,330,238,221,112,171,331,239,219,693,695,696,692,521,66,603,545,154,543,67,519,601,155,544,68,520,602,153,69,541,517,599,157,542,600,70,518,158,71,540,516,598,156,536,512,64,594,152,534,510,65,592,150,535,511,63,593,151,515,539,60,597,148,513,537,61,595,149,514,538,62,596,147,683,688,685,681,655,188,659,657,652,641,186,639,643,636,649,187,647,651,644,184,625,623,627,620,633,635,185,631,629,183,617,615,619,612,471,247,194,565,79,469,245,192,563,80,470,246,193,564,81,610,611,190,607,605,244,472,191,566,73,243,473,189,567,72,702,701,698,699,255,208,485,265,276,263,209,256,483,277,264,207,254,484,275,211,261,258,481,272,262,482,212,259,273,210,260,257,480,274,271,253,214,476,282,269,251,215,474,283,270,252,213,475,281,249,267,217,479,278,250,268,218,477,279,248,266,216,478,280,661,667,669,671,306,87,427,319,468,317,88,307,425,466,318,89,305,426,467,90,315,302,423,464,316,424,91,303,465,92,314,304,422,463,310,297,93,418,459,308,298,94,416,457,309,296,95,417,458,300,313,96,421,462,301,311,97,419,460,299,312,98,420,461,677,675,678,674 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#24d4369d63c88701266d916dc6f9c75e12853e26a0a22f3b011b6cf68ccd31bb, 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 15:56:00 · history