Equation 677 Database

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Magma bc08a1b8fcc7…

magma bc08a1b8fcc7
Size
381
Isomorphism class hash
bc08a1b8fcc7d55dc0886c41220cf399d2b289704755e3c8b1c8cedc2cf1c995
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 23:20:01
Display reorder
380,31,39,57,328,49,6,24,4,22,47,32,40,58,319,50,7,42,25,5,23,33,41,59,320,51,8,43,26,1,18,34,36,54,323,52,9,44,27,0,19,35,37,55,324,53,10,45,28,2,20,30,38,56,46,326,48,11,29,3,21,14,16,17,12,13,15,334,367,333,331,332,330,350,349,368,366,287,290,279,318,271,245,263,265,255,299,282,291,280,321,272,240,294,258,266,256,286,292,281,322,273,241,295,259,267,257,283,293,276,325,274,242,296,260,268,252,284,288,277,327,275,243,297,261,269,253,285,289,278,298,329,270,244,262,264,254,247,249,250,251,246,248,374,373,362,375,344,365,339,355,343,345,208,182,200,305,192,217,235,215,233,190,209,183,201,301,193,218,191,236,210,228,204,184,202,300,194,219,186,237,211,229,205,185,203,302,195,220,187,238,212,230,206,180,198,303,196,221,188,239,213,231,207,181,199,189,304,197,216,234,214,232,225,227,222,223,224,226,360,359,378,379,342,348,364,363,341,361,140,148,132,315,130,155,173,175,165,122,141,149,133,316,131,150,123,168,176,166,142,144,134,317,126,151,124,169,177,167,143,145,135,312,127,152,125,170,178,162,138,146,136,313,128,153,120,171,179,163,139,147,137,121,314,129,154,172,174,164,157,159,160,161,156,158,376,356,357,340,346,358,372,371,347,377,76,78,68,306,60,119,103,111,101,86,77,79,69,307,61,114,87,104,112,96,72,80,70,308,62,115,88,105,113,97,73,81,71,309,63,116,89,106,108,98,74,82,66,310,64,117,84,107,109,99,75,83,67,85,311,65,118,102,110,100,93,95,90,91,92,94,351,352,354,370,336,369,353,338,335,337 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#18304af5f7caa048a8c850a4737239c8b810350baddda3284c82a3ed696abf70, 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 23:20:02 · history