Equation 677 Database

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Magma 42add03fbf33…

magma 42add03fbf33
Size
381
Isomorphism class hash
42add03fbf337ca57130b02f6b94804f283ba41cca68ff9c3dfa90f4c20a20b2
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 23:15:48
Display reorder
380,197,207,202,192,182,187,19,20,54,52,53,212,267,257,262,286,271,276,131,120,126,146,135,140,116,111,290,105,95,100,3,2,26,250,4,5,55,56,57,58,63,217,227,232,237,242,247,297,176,165,171,162,150,156,284,59,62,61,60,222,322,321,323,318,319,320,361,357,347,337,342,376,350,332,365,371,199,209,204,194,184,189,78,79,82,80,81,214,266,256,261,289,274,279,134,124,129,149,139,144,119,114,294,108,99,104,92,90,91,254,93,94,83,84,85,86,87,219,229,234,239,244,249,299,179,169,174,164,154,159,283,88,89,0,1,224,306,308,307,311,309,310,364,359,349,339,344,379,354,334,369,374,196,206,201,190,181,186,31,32,33,34,35,210,268,258,263,287,272,277,132,122,127,147,137,142,117,112,292,106,96,101,48,49,47,252,51,50,7,8,9,6,42,216,225,230,236,240,245,296,177,167,172,160,151,155,280,45,44,46,43,221,304,303,305,301,300,302,360,356,346,335,341,377,352,330,367,372,198,208,203,193,183,188,64,65,68,66,67,213,269,259,264,288,273,278,133,123,128,148,138,143,118,113,293,107,98,103,11,12,10,253,14,13,69,73,70,71,72,218,228,233,238,243,248,298,178,168,173,163,153,158,282,77,75,74,76,223,314,313,312,316,317,315,362,358,348,338,343,378,353,333,368,373,195,205,200,191,180,185,17,18,36,15,16,211,265,255,260,285,270,275,130,121,125,145,136,141,115,110,291,109,97,102,22,23,21,251,25,24,37,38,39,40,41,215,226,231,235,241,246,295,175,166,170,161,152,157,281,27,30,29,28,220,328,327,329,324,325,326,363,355,345,336,340,375,351,331,366,370 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, M = {67} 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 23:15:49 · history