Equation 677 Database

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Magma f240f2848c67…

magma f240f2848c67
Size
705
Isomorphism class hash
f240f2848c674c389f845c08e18d67a545bf32f7feac09700cf9ac2eaf456b1a
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 21:51:26
Display reorder
660,171,307,284,415,516,285,305,413,172,514,173,306,286,414,515,303,174,287,411,512,304,175,288,412,513,302,176,289,410,511,290,298,406,177,507,291,296,404,178,505,292,297,405,179,506,301,293,409,180,510,299,294,407,181,508,300,295,408,182,509,679,684,673,686,74,119,258,242,128,259,117,243,75,126,76,118,257,244,127,122,73,254,245,124,120,71,255,246,125,121,72,256,247,123,249,114,240,65,134,250,115,241,66,132,248,116,239,67,133,113,252,236,68,130,111,253,237,69,131,112,251,238,70,129,665,672,668,671,268,391,29,504,463,27,389,502,266,461,267,390,28,503,462,387,271,25,500,459,388,269,26,501,460,386,270,24,499,458,35,382,495,263,454,33,380,493,264,452,34,381,494,265,453,385,31,498,262,457,383,32,496,260,455,384,30,497,261,456,683,682,677,674,13,653,656,654,659,640,637,638,14,643,12,645,648,646,651,621,16,624,622,627,628,17,632,630,635,613,15,616,614,619,478,107,221,19,601,476,105,219,20,599,477,106,220,18,600,604,607,606,22,608,108,479,222,23,602,109,480,223,21,603,702,700,704,699,86,47,135,190,4,136,45,191,87,5,88,46,137,189,3,43,85,138,193,1,44,83,139,194,0,42,84,140,192,2,141,38,188,77,10,142,36,186,78,11,143,37,187,79,9,41,144,184,80,6,39,145,185,81,7,40,146,183,82,8,692,694,689,695,211,333,475,149,451,473,334,147,212,449,210,332,474,148,450,336,207,471,152,447,337,208,472,150,448,335,209,470,151,446,466,339,155,217,442,464,340,153,218,440,465,338,154,216,441,342,469,158,213,445,343,467,156,214,443,341,468,157,215,444,661,664,663,666,205,569,99,586,367,100,567,584,206,365,204,568,98,585,366,565,201,95,582,363,566,202,96,583,364,564,203,97,581,362,90,560,577,196,358,91,558,575,197,356,89,559,576,195,357,563,93,580,199,361,561,94,578,200,359,562,92,579,198,360,696,690,693,691,273,403,427,319,327,425,401,317,274,328,272,402,426,318,326,399,276,423,315,330,400,277,424,316,331,398,275,422,314,329,418,394,310,279,325,416,392,308,280,323,417,393,309,278,324,397,421,313,282,321,395,419,311,283,322,396,420,312,281,320,675,687,678,680,64,658,655,657,652,639,642,641,62,636,63,650,647,649,644,626,60,623,625,620,634,61,631,633,629,618,59,615,617,612,51,572,519,55,102,52,570,517,53,103,50,571,518,54,104,611,609,610,58,605,573,48,520,56,110,574,49,521,57,101,701,697,703,698,235,557,379,533,492,377,555,531,233,490,234,556,378,532,491,553,231,375,529,488,554,232,376,530,489,552,230,374,528,487,370,548,524,226,483,368,546,522,224,481,369,547,523,225,482,551,373,527,229,486,549,371,525,227,484,550,372,526,228,485,669,667,670,662,169,545,598,439,355,596,543,437,170,353,168,544,597,438,354,541,165,594,435,351,542,166,595,436,352,540,167,593,434,350,589,536,430,160,346,587,534,428,161,344,588,535,429,159,345,539,592,433,163,349,537,590,431,164,347,538,591,432,162,348,681,676,685,688 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#f6b6fc56ae6a00548325e9d66bb78aa16bb0852529ebdb9883eeafc26b8a7eae, 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 21:51:27 · history