Equation 677 Database

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Magma 8bab2b3168f2…

magma 8bab2b3168f2
Size
381
Isomorphism class hash
8bab2b3168f2e1bd47ed2fc4dfafaba3ac4d847eb79a97ae936815a4d3292974
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 23:34:00
Display reorder
380,156,161,157,158,159,160,256,267,276,286,296,246,280,290,240,250,260,270,12,13,14,15,16,17,21,22,23,18,19,20,162,163,164,165,166,167,124,125,120,121,122,123,131,126,127,128,129,130,316,317,312,313,314,315,220,230,181,191,200,210,229,215,235,185,195,205,371,363,334,360,358,351,352,357,376,335,175,174,176,177,178,179,258,268,278,288,298,248,283,293,243,253,263,273,68,69,70,71,66,67,64,65,60,61,62,63,169,170,171,172,173,168,154,155,150,151,152,153,149,144,145,146,147,148,308,309,310,311,306,307,222,232,182,192,202,212,227,218,238,188,198,208,373,367,341,365,331,356,355,359,378,342,42,47,43,44,45,46,252,262,272,282,292,242,284,294,244,254,264,274,139,140,141,142,143,138,137,132,133,134,135,136,39,40,41,36,37,38,74,75,76,77,72,73,78,79,80,81,82,83,318,319,320,321,322,323,223,233,183,193,203,213,221,211,231,180,190,201,374,364,354,369,330,343,344,338,372,353,119,118,114,115,116,117,259,269,279,289,299,249,281,291,241,251,261,271,104,105,106,107,102,103,100,101,96,97,98,99,112,113,108,109,110,111,31,32,33,34,35,30,28,29,24,25,26,27,325,326,327,328,329,324,225,236,186,196,206,216,228,219,239,189,199,209,370,368,347,361,349,336,337,350,379,348,55,54,56,57,58,59,255,265,275,285,295,245,287,297,247,257,266,277,84,85,86,87,88,89,93,94,95,90,91,92,49,50,51,52,53,48,2,3,4,5,1,0,6,7,8,9,10,11,304,305,301,300,302,303,226,237,187,197,207,217,224,214,234,184,194,204,377,362,345,366,339,332,333,340,375,346 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {73} 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 23:34:01 · history