Equation 677 Database

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Magma aa5944309d6e…

magma aa5944309d6e
Size
705
Isomorphism class hash
aa5944309d6e7c278e2ef4edf5be6b3ee0a3aa4cdda4d3e9b70897e3fe167553
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 21:15:08
Display reorder
660,450,522,498,402,119,451,523,117,499,403,452,524,118,500,404,453,525,115,501,405,454,526,116,502,406,455,527,114,503,407,448,520,110,496,400,449,521,108,497,401,495,447,519,109,399,444,516,113,492,396,445,517,111,493,397,446,518,112,494,398,684,677,686,680,46,426,191,172,268,47,427,269,189,173,45,428,267,190,171,42,429,264,187,168,43,430,265,188,169,44,431,266,186,170,37,424,274,182,178,38,425,275,180,179,181,36,423,273,177,40,420,270,185,174,41,421,271,183,175,39,422,272,184,176,671,668,665,663,474,138,546,283,34,475,139,35,547,284,476,140,33,548,282,477,141,30,549,286,478,142,31,550,287,479,143,32,551,285,472,136,25,544,281,473,137,26,545,279,543,471,135,24,280,468,132,28,540,277,469,133,29,541,278,470,134,27,542,276,687,683,679,681,616,614,617,612,300,624,622,301,625,620,632,630,302,633,628,640,638,303,641,636,648,646,304,649,645,656,654,305,657,653,600,598,306,601,596,608,606,307,609,604,593,592,590,308,588,566,564,309,569,568,576,574,310,577,573,584,583,311,585,581,703,700,702,704,125,378,221,366,20,123,379,18,219,367,124,380,19,220,368,121,381,23,217,369,122,382,21,218,370,120,383,22,216,371,131,376,15,227,364,129,377,16,225,365,226,130,375,17,363,127,372,14,223,360,128,373,12,224,361,126,374,13,222,362,694,691,692,689,414,510,462,438,62,415,511,60,463,439,416,512,61,464,440,417,513,65,465,441,418,514,63,466,442,419,515,64,467,443,412,508,68,460,436,413,509,66,461,437,459,411,507,67,435,408,504,71,456,432,409,505,69,457,433,410,506,70,458,434,667,666,669,664,330,148,51,91,250,331,149,251,52,92,332,147,249,53,90,333,144,246,50,94,334,145,247,48,95,335,146,248,49,93,328,154,241,57,89,329,155,242,58,87,59,327,153,240,88,324,150,244,56,85,325,151,245,54,86,326,152,243,55,84,693,695,696,690,106,78,486,558,213,107,79,214,487,559,105,80,215,488,560,102,81,212,489,561,103,82,210,490,562,104,83,211,491,563,97,76,204,484,556,98,77,205,485,557,483,96,75,206,555,100,72,207,480,552,101,73,208,481,553,99,74,209,482,554,682,688,676,678,613,618,619,615,293,621,626,291,627,623,629,634,292,635,631,637,642,289,643,639,644,650,290,651,647,652,658,288,659,655,597,602,299,603,599,605,610,297,611,607,595,589,594,298,591,570,571,295,567,565,572,578,296,579,575,582,586,294,587,580,699,701,697,698,323,156,534,354,262,321,157,263,535,355,322,158,261,536,356,319,159,258,537,357,320,160,259,538,358,318,161,260,539,359,314,162,253,532,352,312,163,254,533,353,531,313,164,252,351,317,165,256,528,348,315,166,257,529,349,316,167,255,530,350,672,662,661,670,194,342,390,233,2,192,343,1,391,231,193,344,0,392,232,197,345,5,393,229,195,346,3,394,230,196,347,4,395,228,200,340,8,388,239,198,341,6,389,237,387,199,339,7,238,203,336,11,384,235,201,337,9,385,236,202,338,10,386,234,675,685,673,674 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#e0ddb86ffdf58ba66baf4adb67528755a1dfe5eefeff33f7cfcb062fa9d34ece, 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 21:15:09 · history