Equation 677 Database

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Magma 18fe00a83ae2…

magma 18fe00a83ae2
Size
381
Isomorphism class hash
18fe00a83ae27774d3a479391c76d84b7dc036b39c9e1080d43a2cb4be1716b8
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 23:24:58
Display reorder
380,167,192,172,177,182,187,142,147,152,157,162,137,300,302,303,304,305,301,37,42,47,292,27,32,117,122,127,132,107,112,252,227,232,237,242,247,67,72,52,57,62,297,2,287,17,22,7,12,222,197,202,207,212,217,82,92,77,97,102,87,257,267,282,272,277,262,366,332,370,375,357,337,342,347,361,350,168,193,173,178,183,188,143,148,153,158,163,138,320,321,322,317,318,319,38,43,48,293,28,33,118,123,128,133,108,113,253,228,233,238,243,248,68,73,53,58,63,298,3,288,18,23,8,13,223,198,203,208,213,218,83,93,78,98,103,88,258,268,283,273,278,263,365,331,373,378,358,335,340,345,362,354,169,194,174,179,184,189,144,149,154,159,164,139,315,316,311,312,313,314,39,44,49,294,29,34,119,124,129,134,109,114,254,229,234,239,244,249,69,74,54,59,64,299,4,289,19,24,9,14,224,199,204,209,214,219,84,94,79,99,104,89,259,269,284,274,279,264,367,334,372,379,359,339,344,349,363,353,166,190,170,175,180,185,141,146,151,156,161,135,310,307,306,329,308,309,36,40,45,291,26,31,115,121,126,131,106,110,250,226,230,235,240,245,65,70,51,56,61,296,0,286,16,21,5,11,221,195,201,206,211,216,80,90,76,95,100,85,255,266,281,271,276,261,368,333,371,377,355,338,343,348,360,352,165,191,171,176,181,186,140,145,150,155,160,136,324,325,326,327,328,323,35,41,46,290,25,30,116,120,125,130,105,111,251,225,231,236,241,246,66,71,50,55,60,295,1,285,15,20,6,10,220,196,200,205,210,215,81,91,75,96,101,86,256,265,280,270,275,260,369,330,374,376,356,336,341,346,364,351 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#4ff69c35f55aa106c20b4528e074e3f72eddedd150e00069ea529e91bc9e2010, M = {68} 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 23:24:59 · history