Equation 677 Database

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Magma 20c723355964…

magma 20c723355964
Size
381
Isomorphism class hash
20c723355964df9e48a6f5d7b300297cccb6d680a480204be266ddf5fa02be23
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 23:24:46
Display reorder
380,194,189,199,204,209,184,289,294,299,274,279,284,219,224,229,234,239,214,300,302,303,304,305,301,114,119,94,99,104,109,154,159,164,169,174,179,244,249,254,259,264,269,69,74,79,84,89,64,59,34,39,44,49,54,29,9,24,14,19,4,139,149,134,124,129,144,354,376,366,363,337,332,342,356,340,371,192,187,197,202,207,182,285,291,297,270,275,280,217,222,227,232,237,212,317,312,313,314,315,316,112,117,92,97,102,107,152,157,162,167,172,177,242,247,252,257,262,267,67,72,77,82,87,62,57,32,37,42,47,52,27,7,22,12,17,2,137,147,132,122,127,142,351,375,365,360,336,352,349,355,350,370,190,185,196,201,206,180,287,290,296,272,277,282,216,221,226,231,235,211,328,324,329,325,326,327,111,115,91,96,101,106,151,156,161,166,171,176,240,245,250,256,261,266,65,70,75,80,85,61,55,31,36,41,46,50,25,5,20,10,15,0,136,145,131,121,126,140,348,378,368,361,341,346,335,359,347,373,193,188,198,203,208,183,288,292,298,273,278,283,218,223,228,233,238,213,306,307,308,309,310,311,113,118,93,98,103,108,153,158,163,168,173,178,243,248,253,258,263,268,68,73,78,83,88,63,58,33,38,43,48,53,28,8,23,13,18,3,138,148,133,123,128,143,353,377,367,364,338,339,344,357,333,372,191,186,195,200,205,181,286,293,295,271,276,281,215,220,225,230,236,210,318,319,320,321,322,323,110,116,90,95,100,105,150,155,160,165,170,175,241,246,251,255,260,265,66,71,76,81,86,60,56,30,35,40,45,51,26,6,21,11,16,1,135,146,130,120,125,141,334,379,369,362,330,343,345,358,331,374 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 = {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 23:24:47 · history