Equation 677 Database

← all  ·  ← by size  ·  ← size 707

Magma 2c94b2dce909…

magma 2c94b2dce909
Size
707
Isomorphism class hash
2c94b2dce909df2fdaafa9a34d5faa728f3b9dc0ca9602ff6b2ccca6a1df2688
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 23:29:29
Display reorder
364,363,365,362,361,360,642,7,9,8,11,6,10,152,151,153,154,155,150,80,79,81,82,83,78,91,90,92,93,94,95,166,165,167,162,163,164,325,324,326,327,328,329,291,290,292,293,288,289,331,330,332,333,334,335,341,340,336,337,338,339,140,142,139,143,138,141,236,235,237,238,239,234,357,356,359,358,354,355,480,479,481,482,483,484,457,456,455,459,460,458,443,445,444,448,446,447,570,572,571,574,575,573,563,562,561,560,558,559,418,417,419,415,416,414,409,408,410,413,411,412,421,420,422,423,424,425,616,630,627,631,617,629,632,628,678,686,651,681,703,677,700,696,699,705,693,706,321,323,322,319,320,318,287,286,282,283,284,285,40,39,41,36,37,38,123,122,124,125,120,121,265,264,266,268,267,269,181,180,182,183,184,185,4,3,5,1,0,2,177,176,178,179,174,175,275,274,271,270,272,273,219,221,218,216,217,220,187,186,188,189,190,191,194,193,195,196,197,192,588,590,589,593,591,592,599,598,597,595,596,594,578,577,576,580,581,579,543,545,544,541,542,540,429,431,430,426,427,428,584,583,582,587,585,586,406,405,407,404,402,403,539,538,537,535,536,534,624,615,614,626,625,613,606,623,680,675,670,662,704,665,672,661,692,695,664,701,207,209,208,205,206,204,250,249,251,246,247,248,233,232,228,229,230,231,226,225,227,222,223,224,107,106,102,103,104,105,253,252,254,255,256,257,310,309,311,306,307,308,313,312,314,315,316,317,281,280,276,277,278,279,27,29,26,24,25,28,97,96,98,99,100,101,75,74,76,77,72,73,515,514,513,511,512,510,509,508,507,505,506,504,548,547,546,550,551,549,518,517,516,519,520,521,492,494,493,495,496,497,499,498,500,502,503,501,491,442,441,438,439,440,605,604,603,600,602,601,608,609,612,621,611,607,622,610,658,691,674,669,694,657,668,676,690,685,650,702,19,21,20,23,18,22,300,305,301,302,303,304,108,113,109,110,111,112,295,294,296,297,298,299,262,261,263,258,259,260,30,35,31,32,33,34,200,199,201,202,203,198,42,47,43,44,45,46,135,134,136,137,132,133,129,131,128,126,127,130,114,119,115,116,117,118,211,210,212,213,214,215,523,522,524,525,526,527,532,531,533,528,529,530,386,385,384,388,389,387,383,382,381,378,379,380,400,399,401,397,398,396,391,390,392,394,395,393,372,374,373,376,377,375,437,436,435,433,434,432,620,634,635,644,643,619,633,618,663,697,648,684,687,655,671,673,679,688,660,698,351,353,352,348,350,349,62,61,63,64,65,60,66,71,67,68,69,70,146,145,147,148,149,144,55,54,56,57,58,59,50,49,51,52,53,48,173,172,168,169,170,171,240,245,241,242,243,244,86,85,87,88,89,84,345,347,344,343,342,346,161,160,156,157,158,159,13,12,14,15,16,17,568,567,569,564,565,566,474,473,475,476,477,478,451,450,449,453,454,452,556,555,557,554,552,553,488,490,489,485,486,487,463,462,461,466,464,465,468,467,469,472,470,471,367,366,368,369,370,371,638,639,637,636,640,641,645,646,666,682,654,659,689,652,653,649,656,667,647,683 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = {72, 73, 74, 75, 76, 77, 127} 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 23:29:30 · history