Equation 677 Database

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Magma fc2544326d0e…

magma fc2544326d0e
Size
705
Isomorphism class hash
fc2544326d0e9f675a56d54a07530062f97778d2bb98254d8e575ad8894e25cc
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 20:47:44
Display reorder
660,514,193,542,462,438,515,191,543,463,439,513,192,541,461,437,189,510,538,458,434,190,511,539,459,435,188,512,540,460,436,533,505,199,453,429,534,506,197,454,430,532,504,198,452,428,508,536,195,456,432,509,537,196,457,433,507,535,194,455,431,681,679,683,685,402,30,366,20,148,403,31,367,21,146,401,29,365,22,147,26,398,362,23,144,27,399,363,24,145,28,400,364,25,143,357,393,36,18,139,358,394,37,19,137,356,392,35,17,138,396,360,32,14,142,397,361,33,15,140,395,359,34,16,141,672,668,664,663,342,202,414,490,44,343,200,415,491,45,341,201,413,489,46,205,338,410,486,47,203,339,411,487,48,204,340,412,488,49,405,333,208,481,42,406,334,206,482,43,404,332,207,480,41,336,408,211,484,38,337,409,209,485,39,335,407,210,483,40,682,674,676,678,650,110,647,645,648,658,111,655,652,656,642,112,639,637,640,109,618,615,613,616,107,626,623,621,624,108,634,631,628,632,70,545,101,68,465,71,546,102,66,466,72,544,103,67,464,599,597,104,600,601,610,606,105,605,608,547,69,106,1,467,703,697,700,704,6,61,154,390,354,7,59,152,391,355,5,60,153,389,353,57,2,157,386,350,58,3,155,387,351,56,4,156,388,352,160,12,52,381,345,158,13,50,382,346,159,11,51,380,344,8,163,55,384,348,9,161,53,385,349,10,162,54,383,347,692,691,689,694,225,165,502,426,330,226,166,503,427,331,224,164,501,425,329,168,228,498,422,326,169,229,499,423,327,167,227,500,424,328,493,231,171,417,321,494,232,172,418,322,492,230,170,416,320,234,496,174,420,324,235,497,175,421,325,233,495,173,419,323,665,662,661,667,116,90,294,283,262,117,88,295,281,260,118,89,293,282,261,86,115,290,279,265,87,113,291,280,263,85,114,292,278,264,285,122,96,274,268,286,123,94,272,266,284,124,95,273,267,121,288,92,277,271,119,289,93,275,269,120,287,91,276,270,693,695,696,690,306,218,450,530,594,307,219,451,531,595,305,220,449,529,593,221,302,446,526,590,222,303,447,527,591,223,304,448,528,592,441,297,216,521,585,442,298,217,522,586,440,296,215,520,584,300,444,212,524,588,301,445,213,525,589,299,443,214,523,587,684,688,675,680,651,134,644,649,646,659,135,653,657,654,643,136,636,641,638,133,619,612,617,614,131,627,620,625,622,132,635,629,633,630,65,570,125,517,99,63,568,126,518,97,64,569,127,516,98,603,602,128,598,596,611,604,129,609,607,571,62,130,519,100,699,698,702,701,564,74,565,478,582,566,75,567,479,583,562,73,563,477,581,77,556,557,474,578,78,558,559,475,579,76,561,560,476,580,0,150,80,469,573,549,548,81,470,574,151,149,79,468,572,553,552,83,472,576,555,554,84,473,577,550,551,82,471,575,666,671,670,669,378,178,318,258,247,379,176,319,259,245,377,177,317,257,246,181,374,314,254,243,179,375,315,255,244,180,376,316,256,242,309,369,184,249,238,310,370,182,250,236,308,368,183,248,237,372,312,187,252,241,373,313,185,253,239,371,311,186,251,240,673,686,677,687 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#d5c298f3996cbe1c131ede943bdfb3db88b47e8bf729cba865448336ce4ceccf, 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 20:47:44 · history