Equation 677 Database

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Magma 8b9b0f0bc29e…

magma 8b9b0f0bc29e
Size
381
Isomorphism class hash
8b9b0f0bc29e8ad4dd3709917775c355c0154b8f14e1a73a83e1f4b2b6189af8
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 23:34:49
Display reorder
380,154,149,159,134,139,144,224,229,234,239,244,249,214,219,209,199,204,310,311,309,307,308,306,23,29,34,14,284,19,259,264,254,273,279,64,69,294,74,79,84,124,129,119,109,114,9,299,8,90,99,85,164,169,174,179,184,189,59,289,54,44,49,269,194,104,39,334,364,374,359,344,354,379,349,339,369,153,148,158,133,138,143,222,227,232,237,242,247,212,217,207,197,202,319,320,318,322,323,321,20,28,33,13,283,18,257,262,252,274,276,63,68,293,73,78,83,122,128,118,108,113,5,297,4,93,97,88,162,167,172,177,182,187,58,288,53,43,48,266,192,103,38,332,362,372,356,343,352,377,348,338,367,152,147,157,131,135,140,223,228,233,238,243,248,213,218,208,198,203,325,326,324,328,329,327,21,27,30,12,282,17,258,263,253,272,278,60,65,291,71,75,80,123,127,117,107,112,2,295,0,91,95,87,163,168,173,178,183,188,55,286,51,40,45,268,193,102,36,333,363,373,358,340,350,378,346,337,368,151,146,155,130,137,141,221,226,231,235,240,246,210,215,205,196,201,300,302,301,304,305,303,24,25,31,11,280,16,256,261,251,271,275,61,66,290,70,76,81,121,125,116,105,110,1,296,3,92,96,86,161,166,171,175,180,185,56,285,50,41,46,267,191,100,35,330,360,370,355,341,351,375,345,336,366,150,145,156,132,136,142,220,225,230,236,241,245,211,216,206,195,200,314,312,313,317,315,316,22,26,32,10,281,15,255,260,250,270,277,62,67,292,72,77,82,120,126,115,106,111,7,298,6,94,98,89,160,165,170,176,181,186,57,287,52,42,47,265,190,101,37,331,361,371,357,342,353,376,347,335,365 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 = {72} 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 23:34:50 · history