Equation 677 Database

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Magma 0f836a7e31d4…

magma 0f836a7e31d4
Size
705
Isomorphism class hash
0f836a7e31d4ddaab5e49ea501c664204ae0c70a821cd51239be1deb1e497a4b
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 17:24:40
Display reorder
660,40,555,423,9,399,41,424,10,556,400,39,557,425,11,401,554,36,422,8,398,552,37,420,6,396,553,38,421,7,397,414,546,1,46,390,415,547,0,47,391,416,548,2,45,392,549,417,3,42,393,550,418,4,43,394,551,419,5,44,395,679,677,685,687,94,483,363,343,202,95,364,344,484,203,93,485,365,342,201,482,97,362,346,205,480,98,360,347,206,481,96,361,345,204,354,474,349,100,208,355,475,350,101,209,356,476,348,99,207,477,357,352,103,211,478,358,353,104,212,479,359,351,102,210,664,661,667,669,15,519,495,327,144,16,496,328,520,145,17,521,497,329,146,518,14,494,326,143,516,12,492,324,141,517,13,493,325,142,486,510,318,21,150,487,511,319,22,151,488,512,320,23,152,513,489,321,20,149,514,490,322,18,147,515,491,323,19,148,683,688,684,675,82,640,639,641,643,83,647,649,648,651,81,656,655,657,659,632,78,631,633,635,616,79,615,617,619,624,80,623,625,627,84,253,255,73,587,85,254,256,74,585,86,252,257,72,586,590,589,591,76,592,600,599,601,77,603,608,604,609,75,611,697,704,698,700,225,375,471,180,531,226,472,181,376,532,227,377,473,182,533,374,228,470,179,530,372,229,468,177,528,373,230,469,178,529,462,366,186,231,522,463,367,187,232,523,464,368,188,233,524,369,465,185,234,525,370,466,183,235,526,371,467,184,236,527,693,694,690,689,154,110,582,126,507,155,583,127,108,508,153,109,584,128,509,106,157,581,125,506,107,158,579,123,504,105,156,580,124,505,573,116,117,160,498,574,114,118,161,499,575,115,119,159,500,112,576,120,163,501,113,577,121,164,502,111,578,122,162,503,672,668,671,666,140,49,245,71,543,138,243,69,50,544,139,48,244,70,545,52,136,248,67,542,53,137,246,68,540,51,135,247,66,541,240,55,62,131,534,241,56,60,129,535,242,54,61,130,536,58,239,65,134,537,59,237,63,132,538,57,238,64,133,539,691,695,692,696,193,447,411,567,435,194,412,568,448,436,192,449,413,569,437,446,189,410,566,434,444,190,408,564,432,445,191,409,565,433,402,438,558,199,426,403,439,559,200,427,404,440,560,198,428,441,405,561,195,429,442,406,562,196,430,443,407,563,197,431,678,680,681,686,338,636,642,637,638,336,650,645,644,646,337,653,658,652,654,629,341,634,628,630,612,339,618,613,614,620,340,626,621,622,570,89,91,333,251,571,87,92,334,249,572,88,90,335,250,593,595,594,332,588,596,602,597,330,598,605,610,606,331,607,701,703,702,699,217,275,315,291,264,218,316,292,273,265,216,274,317,293,266,271,213,314,290,267,272,214,312,288,268,270,215,313,289,269,306,281,282,223,262,307,279,283,224,263,308,280,284,222,261,277,309,285,219,258,278,310,286,220,259,276,311,287,221,260,663,665,670,662,174,24,459,387,303,175,460,388,25,304,176,26,461,389,305,27,173,458,386,302,28,171,456,384,300,29,172,457,385,301,450,30,378,165,294,451,31,379,166,295,452,32,380,167,296,33,453,381,168,297,34,454,382,169,298,35,455,383,170,299,682,674,673,676 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#520f0c8ba72cb86fc7f95b2cd25444b775e13567ed9a2b839438811596de084e, 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 17:24:41 · history