Equation 677 Database

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Magma 88a0cac071d2…

magma 88a0cac071d2
Size
595
Isomorphism class hash
88a0cac071d293eb43ae3dd6de2da6cf336a5ea6f0f1f37fb814a7b3e2fd721e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 16:52:05
Display reorder
120,125,121,122,123,124,106,105,107,102,103,104,359,358,357,361,362,360,335,337,336,333,334,332,348,347,349,345,346,344,532,518,530,572,574,276,278,277,280,281,279,241,240,242,243,244,245,257,256,252,253,254,255,158,157,159,160,161,156,165,164,166,167,162,163,184,183,185,180,181,182,291,290,292,293,288,289,229,231,228,232,233,230,152,151,153,154,155,150,75,74,76,77,72,73,316,315,317,314,312,313,401,400,399,397,398,396,414,416,415,413,412,411,355,354,353,352,350,351,485,484,507,506,482,483,403,481,448,480,447,479,529,515,527,525,524,521,567,571,568,590,582,592,585,583,565,587,2,4,3,1,0,5,44,43,45,46,47,42,302,301,303,304,305,300,275,274,270,271,272,273,51,50,52,53,48,49,141,140,142,143,138,139,218,217,219,220,221,216,174,176,179,177,178,175,284,283,285,286,287,282,247,246,248,249,250,251,458,459,419,497,501,496,494,499,495,493,491,492,505,464,500,463,423,424,475,440,441,443,444,442,377,376,375,378,379,380,402,476,445,477,446,478,526,541,516,517,540,539,545,564,552,566,570,579,546,586,591,594,136,132,137,134,135,133,131,130,126,127,128,129,189,188,190,191,186,187,88,87,89,84,85,86,27,26,28,29,24,25,215,214,210,211,212,213,11,10,6,7,8,9,32,34,31,35,30,33,39,38,40,41,36,37,12,17,13,14,15,16,404,406,405,408,409,407,364,363,365,366,367,368,321,323,322,320,318,319,327,329,328,324,325,326,489,488,508,418,509,490,462,331,461,504,460,330,536,535,514,528,510,511,556,578,543,562,544,555,561,560,553,573,114,116,115,118,119,117,298,297,299,294,295,296,310,309,311,306,307,308,266,265,267,268,269,264,202,201,203,198,199,200,18,23,19,20,21,22,168,173,169,170,171,172,149,145,148,146,147,144,96,101,97,98,99,100,60,65,61,62,63,64,468,428,427,382,383,381,369,371,370,374,372,373,391,390,392,393,410,429,449,486,417,487,450,451,340,339,338,341,342,343,422,420,502,498,503,421,542,523,522,534,512,520,589,554,576,580,563,569,593,549,558,547,57,59,58,55,56,54,227,226,222,223,224,225,95,94,90,91,92,93,260,259,261,262,263,258,67,66,68,69,70,71,83,82,78,79,80,81,110,109,111,112,113,108,237,239,236,234,235,238,192,197,193,194,195,196,208,207,209,204,205,206,472,436,435,433,434,471,469,431,430,394,432,470,457,456,455,453,454,452,437,473,395,474,438,439,386,385,384,387,388,389,356,467,426,466,425,465,538,537,533,513,519,531,588,550,551,548,584,559,581,577,575,557 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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 = the submagma generated by {18, 24} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 16:52:06 · history