Equation 677 Database

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Magma 166c66e82688…

magma 166c66e82688
Size
381
Isomorphism class hash
166c66e82688657ec14dd82e89fb11dc2317564a10139887fdb83ef6d3c39dfa
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 23:34:29
Display reorder
380,68,284,69,67,224,66,149,139,144,134,124,129,174,179,169,159,164,294,119,114,104,108,99,254,89,94,84,74,79,62,63,61,65,219,269,259,264,289,274,279,214,59,60,58,56,299,244,249,239,229,234,325,323,324,328,326,327,189,194,184,204,209,64,154,57,199,364,339,344,334,359,354,349,369,379,374,54,283,55,53,223,52,148,138,143,133,123,128,173,178,168,158,163,293,118,113,103,107,98,253,88,93,83,73,78,47,48,49,50,218,268,258,263,288,273,278,213,44,45,43,42,298,243,248,238,228,233,300,302,301,304,305,303,188,193,183,203,208,51,153,46,198,363,338,343,333,358,353,348,368,378,373,21,281,20,23,220,22,145,136,141,130,120,125,171,176,166,156,161,291,115,110,101,106,97,251,85,90,80,70,77,19,1,0,2,216,265,255,260,285,270,275,210,11,12,10,8,296,240,246,236,225,231,322,320,321,319,317,318,185,190,180,201,206,3,151,9,196,361,335,341,331,356,351,345,367,377,370,40,282,41,39,222,38,147,137,142,132,122,127,172,177,167,157,162,292,117,112,100,105,95,252,87,92,82,72,76,33,34,35,36,217,267,256,262,287,271,277,212,30,31,29,28,297,242,247,237,227,232,310,308,309,307,306,329,187,192,182,202,207,37,152,32,197,362,337,342,332,357,352,347,365,376,372,26,280,27,25,221,24,146,135,140,131,121,126,170,175,165,155,160,290,116,111,102,109,96,250,86,91,81,71,75,15,16,14,18,215,266,257,261,286,272,276,211,4,13,5,6,295,241,245,235,226,230,314,315,316,311,312,313,186,191,181,200,205,17,150,7,195,360,336,340,330,355,350,346,366,375,371 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 = {67} 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 23:34:30 · history