Equation 677 Database

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Magma fed1d8a708f2…

magma fed1d8a708f2
Size
381
Isomorphism class hash
fed1d8a708f235667cdc649838c990e84401f6866f9c24043c1d6c655b729c94
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 23:34:20
Display reorder
380,108,103,294,113,118,123,94,99,89,78,84,254,309,310,311,306,307,69,284,68,67,65,66,138,126,131,153,143,148,234,239,229,249,299,259,264,269,274,279,289,198,188,193,213,203,60,61,64,62,63,224,168,156,161,183,173,178,73,74,219,70,71,244,308,208,72,363,333,359,339,344,349,353,368,373,378,107,102,292,111,117,122,90,95,86,75,83,252,328,329,327,325,326,35,282,34,32,33,36,137,128,133,152,142,147,232,237,228,245,295,255,261,266,270,276,285,197,187,192,212,202,4,2,3,31,5,221,167,158,163,182,172,177,23,24,215,20,21,240,324,207,22,362,332,358,335,341,347,352,367,372,377,109,104,293,110,119,124,91,96,85,79,81,250,312,313,314,315,316,14,281,13,11,12,10,139,129,134,154,144,149,231,236,226,247,296,256,260,265,271,275,286,199,189,194,214,204,1,0,59,57,58,223,169,159,164,184,174,179,56,55,218,54,52,242,317,209,53,364,334,355,338,343,345,354,369,374,379,106,100,291,114,116,121,93,98,88,77,82,253,300,302,301,304,305,51,283,50,48,49,47,135,125,130,151,141,146,233,238,227,248,298,257,262,268,273,278,287,196,186,191,210,200,42,43,44,45,46,222,165,157,162,180,170,175,39,40,217,37,41,243,303,205,38,360,330,357,337,342,348,351,365,371,376,105,101,290,112,115,120,92,97,87,76,80,251,319,320,318,322,323,19,280,18,16,17,15,136,127,132,150,140,145,230,235,225,246,297,258,263,267,272,277,288,195,185,190,211,201,26,27,28,29,30,220,166,155,160,181,171,176,8,9,216,6,25,241,321,206,7,361,331,356,336,340,346,350,366,370,375 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, 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 23:34:21 · history