Equation 677 Database

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Magma af14be351899…

magma af14be351899
Size
399
Isomorphism class hash
af14be351899d94bf41350bcaf4fde37fe3840652de8c77050fbbcda9163208b
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 05:06:56
Display reorder
243,244,245,246,247,248,249,250,251,236,237,238,239,240,241,242,234,235,381,252,1,207,217,208,253,0,218,254,209,2,219,210,255,3,220,211,256,4,221,212,257,5,222,213,258,6,223,214,259,7,224,215,260,8,216,261,9,200,226,262,10,201,227,263,11,202,228,264,12,203,229,265,13,204,230,266,14,205,231,267,15,206,232,268,16,198,233,269,17,199,225,392,386,385,391,119,297,195,333,196,120,298,334,121,197,299,335,189,122,300,336,190,123,301,337,191,124,302,338,192,125,303,339,193,117,304,340,194,118,305,341,112,290,188,326,113,291,180,327,114,292,181,328,115,293,182,329,116,294,183,330,108,295,184,331,109,296,185,332,110,288,186,324,111,289,187,325,384,390,389,383,306,281,102,133,103,307,282,134,308,104,283,126,105,309,284,127,106,310,285,128,107,311,286,129,99,312,287,130,100,313,279,131,101,314,280,132,315,274,95,142,316,275,96,143,317,276,97,135,318,277,98,136,319,278,90,137,320,270,91,138,321,271,92,139,322,272,93,140,323,273,94,141,387,398,397,388,87,349,175,342,176,88,351,344,89,177,353,346,178,81,355,348,179,82,357,350,171,83,359,352,172,84,343,354,173,85,345,356,174,86,347,358,80,367,168,360,72,369,169,362,73,371,170,364,74,373,162,366,75,375,163,368,76,376,164,370,77,361,165,372,78,363,166,374,79,365,167,377,393,395,396,394,59,20,161,50,153,60,21,51,61,154,22,52,155,62,23,53,156,54,24,45,157,55,25,46,158,56,26,47,159,57,18,48,160,58,19,49,68,29,145,43,69,30,146,44,70,31,147,36,71,32,148,37,63,33,149,38,64,34,150,39,65,35,151,40,66,27,152,41,67,28,144,42,380,382,379,378 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#2e2f756a3cafada08bba7c237b80b568d8be25212f9eb576d81405e50b413816, 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 05:06:57 · history