Equation 677 Database

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Magma 9f3bfcb06d9c…

magma 9f3bfcb06d9c
Size
381
Isomorphism class hash
9f3bfcb06d9c811c32d21f4cc2e30266f2a6eff44762449980da7a42618d45c0
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:49:15
Display reorder
380,322,164,162,133,127,136,126,155,134,167,154,75,82,187,88,185,323,179,177,94,77,186,321,204,202,108,102,100,110,213,109,210,211,242,319,227,60,54,63,52,236,61,226,234,255,320,253,11,5,13,3,264,12,250,262,318,280,278,27,30,29,26,288,28,276,287,335,334,358,361,332,360,355,330,359,333,314,160,169,148,142,149,141,174,125,163,171,86,99,199,76,198,312,195,194,98,87,178,313,220,219,123,117,116,124,224,101,223,203,241,317,240,51,69,74,68,249,53,248,228,270,315,269,2,19,24,18,274,4,273,254,316,295,294,43,46,45,47,299,44,298,279,351,350,375,378,348,377,379,354,376,349,301,159,158,135,138,139,145,172,143,173,168,93,84,193,89,188,300,192,191,81,97,176,302,217,216,111,113,120,114,218,118,212,200,232,303,238,62,65,66,72,244,70,235,239,260,304,267,0,15,16,22,251,20,263,268,305,285,292,25,37,36,48,277,49,289,293,342,341,356,368,331,367,369,353,357,352,306,157,153,144,140,137,132,156,128,150,151,80,83,189,78,175,307,190,184,91,85,180,308,215,209,119,115,107,112,214,103,201,205,237,309,233,71,67,64,59,243,55,229,225,266,310,261,21,17,14,10,265,6,256,252,311,291,286,31,34,33,35,290,32,281,275,339,338,362,365,336,364,366,340,363,337,324,152,165,146,129,147,130,170,131,166,161,92,96,197,79,196,325,181,182,95,90,183,326,206,207,121,104,105,122,222,106,221,208,247,327,230,50,56,73,57,246,58,245,231,257,328,258,1,7,23,8,272,9,271,259,329,282,283,39,42,41,38,297,40,296,284,347,346,371,374,344,373,370,343,372,345 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#ec3ba3023855818e5e528ebda394e129bb22176ad81db09a2866796bb5a66f68, 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 23:49:16 · history