Equation 677 Database

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Magma 689e7d4cbb4e…

magma 689e7d4cbb4e
Size
705
Isomorphism class hash
689e7d4cbb4efaedb7a28bcaeebdc7630223683e13991f91e4f22e5b47553216
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 18:12:12
Display reorder
660,539,145,297,120,427,540,428,146,298,118,147,429,541,299,119,538,144,426,296,123,536,142,424,294,121,537,143,425,295,122,151,433,303,545,126,434,152,304,546,124,547,435,153,305,125,150,432,302,544,129,148,430,300,542,127,149,431,301,543,128,678,681,682,675,309,263,195,333,495,310,496,261,193,334,262,497,311,194,335,308,259,494,191,332,306,260,492,192,330,307,258,493,190,331,269,501,201,315,339,502,267,199,316,340,317,503,268,200,341,265,500,197,314,338,266,498,198,312,336,264,499,196,313,337,670,662,663,661,367,78,483,273,321,368,322,76,484,274,77,323,369,485,275,366,81,320,482,272,364,79,318,480,270,365,80,319,481,271,73,327,489,373,279,328,74,490,374,280,375,329,75,491,281,72,326,488,372,278,70,324,486,370,276,71,325,487,371,277,676,677,674,679,359,206,355,241,344,360,342,207,353,242,205,343,361,354,240,358,202,347,351,244,356,203,345,352,245,357,204,346,350,243,212,639,637,640,638,647,213,644,648,646,656,655,211,652,654,208,628,629,633,632,209,348,33,362,239,210,349,32,363,238,698,697,704,703,154,136,551,65,439,155,440,137,552,66,138,441,156,553,64,157,139,438,550,68,158,140,436,548,69,159,141,437,549,67,134,445,557,160,63,446,135,558,161,61,162,447,133,559,62,130,444,556,163,59,131,442,554,164,60,132,443,555,165,58,690,693,689,694,451,237,403,471,46,452,47,235,404,472,236,48,453,405,473,450,233,49,402,470,448,234,50,400,468,449,232,51,401,469,228,52,409,457,477,53,226,410,458,478,459,54,227,411,479,231,55,408,456,476,229,56,406,454,474,230,57,407,455,475,672,668,669,665,610,180,399,89,611,612,613,178,397,90,179,615,614,398,88,608,183,609,395,92,604,181,605,396,93,606,182,607,394,91,186,622,390,623,87,624,184,388,625,85,627,626,185,389,86,189,620,393,621,83,187,616,391,617,84,188,618,392,619,82,696,695,692,691,515,103,106,587,586,516,588,104,107,589,105,590,517,108,591,514,102,584,109,585,512,100,580,110,581,513,101,582,111,583,94,599,112,521,598,601,95,113,522,600,523,603,96,114,602,97,597,115,520,596,98,593,116,518,592,99,595,117,519,594,685,680,686,673,575,27,507,463,3,576,4,28,508,464,26,5,577,509,465,574,30,2,506,462,572,31,1,504,460,573,29,0,505,461,25,636,642,643,641,645,23,650,651,649,659,653,24,658,657,21,634,635,631,630,22,6,510,578,466,20,7,511,579,467,701,702,699,700,254,222,379,527,415,252,416,220,380,528,221,417,253,381,529,257,225,414,378,526,255,223,412,376,524,256,224,413,377,525,217,421,385,249,533,422,218,386,250,534,251,423,219,387,535,216,420,384,248,532,214,418,382,246,530,215,419,383,247,531,666,667,671,664,41,166,14,563,287,42,285,167,15,564,168,286,40,16,565,44,169,283,17,562,45,170,284,18,560,43,171,282,19,561,172,293,12,39,569,291,173,13,37,570,38,292,174,11,571,175,289,8,35,568,176,290,9,36,566,177,288,10,34,567,684,687,683,688 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#69e303b0df9a949f679bcb1932ca3e0d44707fb71c41006ed01ea0a3f8179ab7, 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 18:12:13 · history