Equation 677 Database

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Magma 481b59eb5e1c…

magma 481b59eb5e1c
Size
705
Isomorphism class hash
481b59eb5e1c2cc569b8ecb960cd28177db64b6bd8eed29c79e3392e7edcd850
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 21:46:11
Display reorder
660,351,457,385,237,319,238,458,352,386,317,456,236,350,384,318,354,240,460,388,315,355,241,461,389,316,353,239,459,387,314,463,357,235,391,325,464,358,233,392,323,462,356,234,390,324,466,360,231,394,321,361,467,232,395,322,359,465,230,393,320,676,678,674,681,16,146,161,48,513,46,144,17,159,514,145,47,18,160,512,15,44,149,157,516,13,45,147,158,517,14,43,148,156,515,141,7,54,152,519,142,8,52,150,520,143,9,53,151,518,140,10,50,155,522,11,138,51,153,523,12,139,49,154,521,670,672,666,661,373,339,469,164,327,162,340,374,470,328,338,163,372,468,326,376,167,342,472,330,377,165,343,473,331,375,166,341,471,329,345,379,170,475,333,346,380,168,476,334,344,378,169,474,332,348,382,173,478,336,383,349,171,479,337,381,347,172,477,335,677,682,673,675,210,188,493,59,367,60,186,208,494,365,187,58,209,492,366,213,55,191,496,363,211,56,189,497,364,212,57,190,495,362,194,216,65,499,371,192,214,66,500,369,193,215,64,498,370,644,646,61,649,648,656,655,62,658,657,217,195,63,501,368,704,699,698,703,525,244,597,96,481,97,242,526,598,482,243,95,524,596,480,528,92,247,600,484,529,93,245,601,485,527,94,246,599,483,250,531,102,603,487,248,532,103,604,488,249,530,101,602,486,253,534,98,606,490,535,251,99,607,491,533,252,100,605,489,692,694,690,691,561,421,397,200,179,201,422,562,398,177,420,199,560,396,178,564,196,424,400,175,565,197,425,401,176,563,198,423,399,174,427,567,206,403,185,428,568,207,404,183,426,566,205,402,184,430,570,202,406,181,571,431,203,407,182,569,429,204,405,180,668,662,665,664,282,301,262,33,277,31,299,283,260,275,300,32,281,261,276,278,36,297,265,273,279,34,298,263,274,280,35,296,264,272,292,288,39,257,268,290,289,37,258,266,291,287,38,259,267,295,284,42,256,271,285,293,40,254,269,286,294,41,255,270,689,695,696,693,585,313,633,127,433,125,311,586,634,434,312,126,584,632,432,588,123,309,636,436,589,124,310,637,437,587,122,308,635,435,304,591,118,639,439,302,592,116,640,440,303,590,117,638,438,307,594,121,642,442,595,305,119,643,443,593,306,120,641,441,686,688,679,683,134,84,503,78,5,76,82,132,504,6,83,77,133,502,4,137,74,80,506,0,135,75,81,507,2,136,73,79,505,3,88,129,69,509,91,86,130,67,510,89,87,131,68,508,90,650,651,72,647,645,654,652,70,659,653,128,85,71,511,1,697,700,701,702,409,573,549,21,621,19,574,410,550,622,572,20,408,548,620,412,24,576,552,624,413,22,577,553,625,411,23,575,551,623,579,415,27,555,627,580,416,25,556,628,578,414,26,554,626,582,418,30,558,630,419,583,28,559,631,417,581,29,557,629,663,667,671,669,537,609,223,110,445,111,610,538,221,446,608,112,536,222,444,540,113,612,219,448,541,114,613,220,449,539,115,611,218,447,615,543,108,229,451,616,544,109,227,452,614,542,107,228,450,618,546,104,225,454,547,619,105,226,455,545,617,106,224,453,685,684,680,687 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, 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 21:46:12 · history