Equation 677 Database

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Magma 6bf420914bd1…

magma 6bf420914bd1
Size
399
Isomorphism class hash
6bf420914bd15265d94bd91e1c76b122d029566c6527253ffb6609ec17f40d79
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 12:04:02
Display reorder
237,238,239,240,241,242,234,235,236,246,247,248,249,250,251,243,244,245,381,252,73,94,226,95,253,74,227,96,254,75,228,97,255,76,229,98,256,77,230,90,257,78,231,91,258,79,232,92,259,80,233,93,260,72,225,261,82,103,219,262,83,104,220,263,84,105,221,264,85,106,222,265,86,107,223,266,87,99,224,267,88,100,216,268,89,101,217,269,81,102,218,392,386,385,391,214,297,0,333,2,215,298,334,3,207,299,335,4,208,300,336,5,209,301,337,6,210,302,338,7,211,303,339,8,212,304,340,1,213,305,341,198,290,10,326,199,291,11,327,200,292,12,328,201,293,13,329,202,294,14,330,203,295,15,331,204,296,16,332,205,288,17,324,206,289,9,325,384,390,389,383,306,281,159,30,160,307,282,31,161,308,283,32,153,309,284,33,154,310,285,34,155,311,286,35,156,312,287,27,157,313,279,28,158,314,280,29,315,274,152,23,316,275,144,24,317,276,145,25,318,277,146,26,319,278,147,18,320,270,148,19,321,271,149,20,322,272,150,21,323,273,151,22,387,398,397,388,136,349,188,342,180,137,351,344,181,138,353,346,182,139,355,348,183,140,357,350,184,141,359,352,185,142,343,354,186,143,345,356,187,135,347,358,129,367,197,360,130,369,189,362,131,371,190,364,132,373,191,366,133,375,192,368,134,376,193,370,126,361,194,372,127,363,195,374,128,365,196,377,393,395,396,394,173,56,39,125,40,174,57,117,41,175,58,118,42,176,59,119,43,177,60,120,44,178,61,121,36,179,62,122,37,171,54,123,38,172,55,124,166,65,48,109,167,66,49,110,168,67,50,111,169,68,51,112,170,69,52,113,162,70,53,114,163,71,45,115,164,63,46,116,165,64,47,108,380,382,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#3d5053a678ac6c34fe544eae0cdfa49b10998cf5c87f946440eca40285defc55, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); 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: 21.

last edited by qawbecrdtey at 2026-10-08 12:04:03 · history