Equation 677 Database

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Magma 32d67a419b1e…

magma 32d67a419b1e
Size
705
Isomorphism class hash
32d67a419b1e9e1f96ab9f10d4dd85f45eb2a0883bd39135f3b322c49f2fddbb
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 19:50:28
Display reorder
660,364,27,7,203,436,8,365,201,437,28,6,29,363,202,435,26,10,360,199,432,24,11,361,200,433,25,9,362,198,434,33,5,209,370,442,34,3,207,371,443,35,4,208,369,441,0,32,205,366,438,2,30,206,367,439,1,31,204,368,440,673,684,676,686,412,282,331,228,340,332,413,229,341,283,330,284,411,230,339,285,334,408,231,336,286,335,409,232,337,287,333,410,233,338,280,329,226,418,346,281,327,227,419,347,279,328,225,417,345,325,276,222,414,342,326,277,223,415,343,324,278,224,416,344,665,666,663,671,77,86,550,295,400,551,75,296,401,84,549,85,76,294,399,89,546,73,298,396,87,547,74,299,397,88,548,72,297,398,92,556,293,83,406,90,557,291,81,407,91,555,292,82,405,552,95,289,79,402,553,93,290,80,403,554,94,288,78,404,680,682,675,674,247,257,260,235,472,258,248,236,473,255,259,256,246,234,471,253,263,250,238,468,254,261,251,239,469,252,262,249,237,470,645,647,241,644,648,653,655,242,652,656,637,639,240,636,640,614,613,244,616,617,623,620,245,621,624,631,628,243,629,632,703,699,697,704,12,448,562,36,424,563,13,37,425,449,561,447,14,38,423,444,558,15,39,420,445,559,16,40,421,446,560,17,41,422,454,568,42,18,430,455,569,43,19,431,453,567,44,20,429,564,450,45,21,426,565,451,46,22,427,566,452,47,23,428,689,694,690,691,381,388,310,99,316,311,382,100,317,389,309,387,383,101,315,384,306,380,98,312,385,307,378,96,313,386,308,379,97,314,394,301,105,372,322,395,302,106,373,323,393,300,107,374,321,304,390,104,375,318,305,391,102,376,319,303,392,103,377,320,669,661,662,664,490,111,130,166,136,131,491,167,137,112,129,113,489,165,135,110,126,486,162,132,108,127,487,163,133,109,128,488,164,134,117,121,157,496,142,118,122,158,497,143,119,120,156,495,141,124,116,160,492,138,125,114,161,493,139,123,115,159,494,140,692,695,696,693,508,586,604,66,478,605,509,67,479,587,603,585,507,68,477,582,600,504,69,474,583,601,505,70,475,584,602,506,71,476,592,610,64,514,484,593,611,65,515,485,591,609,63,513,483,606,588,60,510,480,607,589,61,511,481,608,590,62,512,482,679,688,677,685,598,501,542,177,185,540,599,178,183,502,541,503,597,179,184,500,545,594,176,181,498,543,595,174,182,499,544,596,175,180,649,650,168,651,646,657,658,169,659,654,641,642,170,643,638,619,618,171,615,612,626,625,172,627,622,634,633,173,635,630,702,701,698,700,574,520,273,212,460,274,575,210,461,521,275,519,573,211,459,516,272,570,215,456,517,270,571,213,457,518,271,572,214,458,526,264,218,580,466,527,265,216,581,467,525,266,217,579,465,267,522,221,576,462,268,523,219,577,463,269,524,220,578,464,670,672,667,668,350,152,532,52,194,533,348,53,192,150,531,151,349,51,193,155,528,353,48,197,153,529,351,49,195,154,530,352,50,196,147,538,58,356,189,148,539,59,354,190,149,537,57,355,191,534,146,54,359,188,535,144,55,357,186,536,145,56,358,187,678,681,683,687 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#b0c577ef9e4c05d7925e972279aa7c10376825c460b06aa55c85bf856c0bbca9, 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 19:50:29 · history