Equation 677 Database

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Magma d1b794215826…

magma d1b794215826
Size
381
Isomorphism class hash
d1b7942158264e7b5cca8eba5766dd398ae3da8da29f88b6930be8c108c991f4
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 23:44:41
Display reorder
380,38,37,39,40,41,36,251,266,281,296,221,236,65,60,61,62,63,64,42,43,44,45,46,47,324,325,326,327,328,329,143,164,175,190,205,130,200,125,139,163,170,185,220,235,250,265,280,295,191,206,131,144,159,176,70,69,230,245,260,71,66,275,67,290,68,215,370,342,359,356,341,376,375,352,338,337,94,93,95,90,91,92,243,258,273,288,213,228,106,107,102,103,104,105,84,85,86,87,88,89,313,314,315,316,317,312,136,151,166,181,196,120,204,129,142,158,174,189,210,225,240,255,270,286,183,198,123,148,153,168,99,98,234,249,264,100,101,279,96,294,97,219,374,347,357,350,332,368,365,355,345,346,75,74,76,77,72,73,252,267,282,297,222,237,10,5,6,7,4,9,83,78,79,80,81,82,301,300,302,303,304,305,149,156,172,187,202,127,197,122,137,152,167,182,217,232,247,262,277,292,192,207,132,145,160,177,3,2,227,242,257,1,0,272,8,287,11,212,367,330,354,358,331,377,372,351,344,343,118,117,119,114,115,116,244,259,274,289,214,229,52,53,48,49,50,51,108,109,110,111,112,113,320,321,322,323,318,319,140,155,171,186,201,126,195,121,135,150,165,180,216,231,246,261,276,291,184,199,124,138,154,169,55,54,226,241,256,56,57,271,58,285,59,211,366,340,353,362,339,369,371,363,348,349,29,28,24,25,26,27,254,269,284,299,224,239,12,13,14,15,16,17,32,33,34,35,30,31,311,306,307,308,309,310,146,161,178,193,208,133,203,128,141,157,173,188,223,238,253,268,283,298,194,209,134,147,162,179,21,20,233,248,263,22,23,278,18,293,19,218,373,334,360,361,333,379,378,364,336,335 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, M = {70} 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 23:44:42 · history