Equation 677 Database

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Magma 4bd8c8e510a9…

magma 4bd8c8e510a9
Size
705
Isomorphism class hash
4bd8c8e510a9cf9201ecacde823d54284c57e85f3fc4de28635a5a6701e11988
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 21:17:39
Display reorder
660,211,414,342,498,462,212,415,343,499,463,210,416,500,344,464,214,417,345,501,465,215,418,346,502,466,213,419,347,503,467,209,412,340,496,460,207,413,341,497,461,208,411,339,495,459,205,408,336,492,456,206,409,337,493,457,204,410,338,494,458,683,678,685,687,95,143,25,438,223,93,141,26,439,224,94,142,440,24,222,91,139,28,441,226,92,140,29,442,227,90,138,27,443,225,86,134,31,436,221,84,132,32,437,219,85,133,30,435,220,89,137,34,432,217,87,135,35,433,218,88,136,33,434,216,668,671,670,667,43,236,120,244,318,44,234,121,245,319,42,235,243,122,320,46,239,123,240,321,47,237,124,241,322,45,238,125,242,323,41,231,126,250,316,39,232,127,251,317,40,233,128,249,315,37,230,129,246,312,38,228,130,247,313,36,229,131,248,314,674,682,677,681,100,612,618,613,617,101,621,626,620,625,99,629,628,634,633,96,636,642,637,641,97,644,650,645,649,98,653,658,652,657,106,596,602,597,601,107,605,610,604,609,105,588,594,589,593,102,565,567,568,569,103,572,578,573,577,104,580,586,581,585,699,700,703,704,171,270,60,522,366,172,271,61,523,367,173,272,524,62,368,170,273,63,525,369,168,274,64,526,370,169,275,65,527,371,177,268,66,520,364,178,269,67,521,365,179,267,68,519,363,176,264,69,516,360,174,265,70,517,361,175,266,71,518,362,690,693,691,694,167,426,258,330,402,165,427,259,331,403,166,428,332,260,404,163,429,261,333,405,164,430,262,334,406,162,431,263,335,407,158,424,256,328,400,156,425,257,329,401,157,423,255,327,399,161,420,252,324,396,159,421,253,325,397,160,422,254,326,398,666,662,665,663,55,552,553,190,22,56,554,555,191,23,54,556,189,557,21,58,558,559,186,18,59,560,561,187,19,57,562,563,188,20,53,549,548,181,13,51,551,550,182,14,52,547,546,180,12,49,541,540,184,16,50,543,542,185,17,48,545,544,183,15,696,695,689,692,198,486,450,282,294,199,487,451,283,295,200,488,284,452,296,201,489,453,285,297,202,490,454,286,298,203,491,455,287,299,196,484,448,280,292,197,485,449,281,293,195,483,447,279,291,192,480,444,276,288,193,481,445,277,289,194,482,446,278,290,686,684,675,673,79,614,619,615,616,80,622,627,623,624,78,630,631,635,632,82,638,643,639,640,83,646,651,647,648,81,654,659,655,656,77,598,603,599,600,75,606,611,607,608,76,590,595,591,592,73,570,571,564,566,74,574,579,575,576,72,582,587,583,584,701,702,697,698,151,112,354,474,510,152,113,355,475,511,150,111,476,356,512,154,108,357,477,513,155,109,358,478,514,153,110,359,479,515,149,118,352,472,508,147,119,353,473,509,148,117,351,471,507,145,114,348,468,504,146,115,349,469,505,144,116,350,470,506,661,664,672,669,7,390,306,378,534,8,391,307,379,535,6,392,380,308,536,10,393,309,381,537,11,394,310,382,538,9,395,311,383,539,5,388,304,376,532,3,389,305,377,533,4,387,303,375,531,0,384,300,372,528,2,385,301,373,529,1,386,302,374,530,680,676,688,679 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#e3fb677801a83abf4523d8c5dab7d3c82647015c862300302a3edde7221f68e9, 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 21:17:40 · history