Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma 5f35ef9bba3f…

magma 5f35ef9bba3f
Size
707
Isomorphism class hash
5f35ef9bba3fdacd11df76922009448c6d4cae9002cc8abef3a68f6e563530ed
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 10:36:39
Display reorder
184,183,185,180,181,182,706,290,289,291,292,293,288,117,118,119,114,115,116,107,106,102,103,104,105,95,94,90,91,92,93,66,71,67,68,69,70,46,45,47,42,43,44,196,195,197,192,193,194,11,10,6,7,8,9,305,304,301,300,302,303,298,299,294,296,297,295,353,355,354,356,357,358,422,424,423,421,419,420,462,461,463,464,465,466,553,554,552,557,555,556,375,374,376,372,373,371,446,448,447,444,445,443,307,308,306,521,309,310,439,438,437,440,441,442,533,535,534,538,536,537,568,566,565,564,567,569,608,607,611,613,612,610,627,640,638,633,701,684,697,680,696,692,691,704,705,703,233,232,228,229,230,231,128,129,130,131,126,127,226,225,227,222,223,224,34,33,35,30,31,32,208,207,209,204,205,206,145,144,146,147,148,149,61,60,62,63,64,65,259,258,260,261,262,263,163,162,164,165,166,167,250,249,251,246,247,248,519,518,520,516,517,515,417,416,418,413,414,415,363,362,364,359,360,361,491,493,492,496,494,495,411,410,412,408,409,407,404,406,405,402,403,401,489,488,490,485,486,487,323,325,324,327,328,326,337,336,335,339,340,338,572,570,571,575,573,574,616,635,615,636,637,634,614,632,639,623,700,702,699,668,676,675,674,678,681,685,266,264,267,268,269,265,176,177,178,179,174,175,211,210,212,213,214,215,171,170,172,173,168,169,59,58,54,55,56,57,190,189,191,186,187,188,275,274,271,270,272,273,141,140,142,143,138,139,120,125,121,122,123,124,135,134,136,137,132,133,499,498,497,502,500,501,386,388,387,385,383,384,366,365,367,368,369,370,558,559,560,561,562,563,400,399,398,397,395,396,315,314,316,313,311,312,545,544,543,541,542,540,547,548,546,550,551,549,512,514,513,511,509,510,435,434,436,432,433,431,631,628,625,626,630,609,629,646,649,647,689,698,690,670,667,679,669,686,677,693,24,29,25,26,27,28,156,157,158,159,160,161,154,153,155,150,151,152,277,281,276,278,279,280,284,285,287,286,282,283,14,13,15,16,17,12,253,252,254,255,256,257,219,218,220,221,216,217,239,238,234,235,236,237,18,23,19,20,21,22,473,475,474,476,477,478,317,319,318,322,320,321,391,390,389,393,394,392,585,587,586,584,583,582,332,334,333,329,330,331,605,604,603,601,600,602,599,598,597,594,596,595,578,576,577,579,580,581,483,482,484,479,480,481,592,591,593,588,590,589,617,650,641,651,643,642,645,653,644,654,694,682,695,666,673,672,665,687,683,688,39,38,40,41,36,37,0,2,3,4,5,1,200,199,201,202,203,198,75,74,76,77,72,73,78,83,79,80,81,82,85,84,86,87,88,89,101,100,96,97,98,99,51,50,52,53,48,49,110,109,111,112,113,108,245,244,240,241,242,243,378,377,379,381,382,380,345,344,346,341,342,343,507,506,508,503,504,505,525,526,539,524,522,523,470,472,471,467,468,469,530,532,531,528,529,527,455,457,456,460,458,459,452,454,453,450,451,449,350,352,351,349,347,348,429,428,430,426,427,425,652,624,606,618,619,621,622,620,648,655,663,660,664,658,656,659,657,662,661,671 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = {24, 25, 26, 27, 28, 29, 137} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-08 10:36:40 · history