Equation 677 Database

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Magma a1473519199f…

magma a1473519199f
Size
381
Isomorphism class hash
a1473519199f7973426323dd55a98883f5d8747802a6f5b4a4f0b20a5df2785b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:40:17
Display reorder
380,225,246,236,275,256,266,290,99,98,96,97,95,81,185,80,84,82,83,118,119,120,121,122,280,307,308,306,310,311,309,75,76,77,78,79,296,190,195,200,206,211,215,181,286,176,166,174,161,230,220,240,250,260,270,110,109,111,106,107,108,105,103,104,102,101,100,365,346,360,330,340,350,375,356,335,371,227,247,237,277,257,267,291,58,57,55,56,54,140,187,141,137,138,139,51,49,50,53,52,282,328,329,327,325,326,324,134,132,133,136,135,297,193,197,202,207,212,217,182,287,177,167,170,162,232,222,242,252,262,272,12,13,142,16,14,15,64,62,63,61,60,59,367,347,361,332,342,351,377,357,337,370,229,249,239,279,259,269,294,27,28,48,46,47,151,189,150,153,154,152,43,44,45,41,42,284,313,314,312,316,317,315,155,156,157,158,159,299,194,199,204,209,214,219,184,289,179,169,173,164,234,224,244,254,264,274,35,37,36,40,38,39,30,31,29,33,32,34,369,349,364,334,344,354,379,358,339,374,226,245,235,276,255,265,292,5,6,126,124,125,71,186,70,74,72,73,20,19,123,18,17,281,303,304,305,301,300,302,65,66,67,68,69,295,191,196,201,205,210,216,180,285,175,165,171,160,231,221,241,251,261,271,116,115,117,112,113,114,131,129,130,128,127,143,366,345,362,331,341,352,376,355,336,372,228,248,238,278,258,268,293,94,93,91,92,90,0,188,1,4,2,3,87,85,86,89,88,283,321,322,323,318,319,320,144,145,146,147,148,298,192,198,203,208,213,218,183,288,178,168,172,163,233,223,243,253,263,273,8,7,149,9,10,11,23,21,22,26,25,24,368,348,363,333,343,353,378,359,338,373 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {66} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:40:18 · history