Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 71e69f450e16…

magma 71e69f450e16
Size
705
Isomorphism class hash
71e69f450e16dab319af99ba737d050f09f657795ebd20ddd7aad19954a9e7fb
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 17:36:57
Display reorder
660,37,613,603,614,616,38,633,623,634,636,653,654,36,643,656,40,593,583,594,596,553,41,543,554,556,39,573,563,574,576,423,43,433,434,436,443,44,452,453,455,463,42,473,474,476,46,483,493,494,496,47,503,513,514,516,45,523,533,534,536,688,698,700,689,30,600,611,601,617,31,621,631,620,637,641,640,32,651,657,33,580,591,581,597,540,34,551,541,557,35,560,571,561,577,431,28,420,421,437,450,29,442,441,456,471,27,461,460,477,24,491,481,480,497,25,511,500,501,517,26,531,520,521,537,694,699,697,685,22,200,309,369,128,23,198,310,370,126,199,371,21,311,127,18,203,308,368,131,201,19,306,366,129,20,202,307,367,130,300,13,195,360,123,301,14,196,361,124,302,12,197,362,125,16,303,194,363,122,17,304,192,364,120,15,305,193,365,121,673,680,676,666,82,223,285,6,228,83,224,286,7,229,222,8,81,287,230,78,226,284,9,231,227,79,282,10,232,80,225,283,11,233,276,73,221,4,234,277,74,219,5,235,278,72,220,3,236,76,279,217,1,237,77,280,218,0,238,75,281,216,2,239,665,670,668,663,134,618,608,609,602,132,638,628,629,622,658,649,133,648,642,137,598,588,589,582,558,135,548,549,542,136,578,568,569,562,428,140,438,429,422,448,138,459,458,457,468,139,478,469,462,143,488,498,489,482,141,508,518,509,502,142,528,538,529,522,695,701,691,703,246,604,619,607,610,247,624,639,627,630,644,647,248,659,650,249,584,599,587,590,544,250,559,547,550,251,564,579,567,570,439,244,424,427,430,440,245,444,447,449,479,243,464,467,470,240,499,484,487,490,241,519,504,507,510,242,539,524,527,530,704,690,692,702,67,605,612,606,615,68,625,632,626,635,645,646,66,652,655,70,585,592,586,595,545,71,552,546,555,69,565,572,566,575,432,65,425,426,435,451,63,445,446,454,472,64,465,466,475,61,492,485,486,495,62,512,505,506,515,60,532,525,526,535,687,696,686,693,162,273,297,184,417,163,274,298,185,418,275,183,164,299,419,165,272,296,180,416,270,166,294,181,414,167,271,295,182,415,288,160,264,190,408,289,161,265,191,409,290,159,266,189,410,156,291,267,186,411,157,292,268,187,412,158,293,269,188,413,681,684,661,664,205,112,107,84,333,206,113,105,85,334,111,86,204,106,335,208,108,103,87,332,109,209,104,88,330,207,110,102,89,331,98,211,118,90,324,96,212,119,91,325,97,210,117,92,326,214,101,114,93,327,215,99,115,94,328,213,100,116,95,329,662,669,683,678,48,357,321,345,393,49,358,322,346,394,359,347,50,323,395,51,356,320,344,392,354,52,318,342,390,53,355,319,343,391,312,54,348,336,384,313,55,349,337,385,314,56,350,338,386,57,315,351,339,387,58,316,352,340,388,59,317,353,341,389,671,677,672,667,258,405,154,381,174,259,406,155,382,175,407,383,260,153,176,261,404,150,380,177,402,262,151,378,178,263,403,152,379,179,145,256,396,372,172,146,257,397,373,173,144,255,398,374,171,252,148,399,375,168,253,149,400,376,169,254,147,401,377,170,674,675,679,682 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#5aa74a2d4b4bbe4036558963ef968fca94fa5f577bdbfbf2823cea2791e8d20b, 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 17:36:59 · history