Equation 677 Database

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Magma 82cf412ab687…

magma 82cf412ab687
Size
705
Isomorphism class hash
82cf412ab6878532a6f7b299f933af79344dbaa5280c4db3352563cf1caf9079
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 21:56:36
Display reorder
660,596,244,587,593,590,556,245,550,547,553,576,243,570,567,573,656,240,650,647,653,616,241,610,607,613,636,242,630,627,633,250,490,487,496,493,251,510,507,516,513,249,530,527,536,533,470,246,467,476,473,430,247,434,436,435,450,248,447,456,453,698,690,695,691,585,200,591,592,583,545,198,543,551,552,565,199,563,571,572,645,203,643,651,652,605,201,603,611,612,625,202,623,631,632,195,483,491,485,492,196,503,511,505,512,197,523,531,525,532,463,194,471,465,472,426,192,438,437,439,443,193,451,445,452,687,694,701,692,416,18,368,120,217,414,19,218,366,121,415,20,216,367,122,419,21,220,371,123,417,22,221,369,124,418,23,219,370,125,16,223,363,411,126,17,224,364,412,127,15,222,365,413,128,226,12,362,410,129,227,13,360,408,130,225,14,361,409,131,672,679,681,665,278,171,62,271,55,276,172,56,60,272,277,173,54,61,270,281,170,58,65,274,279,168,59,63,275,280,169,57,64,273,177,53,68,284,269,178,51,66,282,267,179,52,67,283,268,49,176,71,287,265,50,174,69,285,266,48,175,70,286,264,667,677,662,673,594,94,586,584,599,554,95,559,546,544,574,93,579,566,564,654,90,659,646,644,614,91,619,606,604,634,92,639,626,624,85,499,486,494,484,86,518,506,514,504,84,539,526,534,524,479,88,466,474,464,433,89,428,431,427,459,87,446,454,444,699,696,688,703,582,40,580,581,598,542,41,558,541,540,562,39,578,560,561,642,36,658,641,640,602,37,618,601,600,622,38,638,621,620,46,498,481,482,480,47,519,501,502,500,45,538,520,522,521,478,42,461,462,460,432,43,423,425,424,458,44,441,442,440,689,704,686,702,588,260,597,595,589,548,258,549,557,555,568,259,569,577,575,648,263,649,657,655,608,261,609,617,615,628,262,629,637,635,255,489,497,488,495,256,509,517,508,515,257,529,537,528,535,469,254,477,468,475,429,252,422,420,421,449,253,457,448,455,700,693,697,685,356,187,320,392,209,354,188,207,318,390,355,186,208,319,391,359,190,205,323,395,357,191,206,321,393,358,189,204,322,394,185,215,315,351,387,183,213,316,352,388,184,214,317,353,389,211,181,314,350,386,212,182,312,348,384,210,180,313,349,385,663,676,671,666,296,81,308,35,161,294,82,159,306,33,295,83,160,307,34,299,80,157,311,31,297,78,158,309,32,298,79,156,310,30,72,167,303,291,26,73,165,304,292,24,74,166,305,293,25,163,75,302,290,29,164,76,300,288,27,162,77,301,289,28,661,682,669,675,5,235,132,117,332,3,236,330,133,118,4,234,331,134,119,0,238,335,135,116,2,239,333,136,114,1,237,334,137,115,233,327,138,11,108,231,328,139,9,109,232,329,140,10,110,326,229,141,7,111,324,230,142,8,112,325,228,143,6,113,668,683,680,664,107,151,404,380,344,105,152,342,402,378,106,150,343,403,379,103,154,347,407,383,104,155,345,405,381,102,153,346,406,382,149,339,399,98,375,147,340,400,96,376,148,341,401,97,377,338,145,398,101,374,336,146,396,99,372,337,144,397,100,373,678,674,684,670 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#fd86fc294900b5ccb814b44936109aa3958b6cd4f65ecf12bfe08854715a531f, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:56:36 · history