Equation 677 Database

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Magma b5837ed5ee3f…

magma b5837ed5ee3f
Size
381
Isomorphism class hash
b5837ed5ee3f1061b4376e7405da18195f861e87f379cac7c03eef662b099c06
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 23:43:20
Display reorder
380,96,82,315,89,117,110,68,103,61,75,97,83,317,76,84,118,111,69,104,62,98,78,306,77,85,119,112,70,105,63,99,79,309,72,86,114,113,71,106,64,100,80,311,73,87,115,108,66,107,65,101,81,74,313,88,116,109,67,102,60,94,90,91,92,93,95,372,343,345,346,344,359,361,371,373,360,193,228,318,235,185,207,220,200,213,227,194,229,327,222,236,180,208,221,201,214,195,230,321,223,237,181,209,216,202,215,196,231,326,224,238,182,204,217,203,210,197,232,319,225,239,183,205,218,198,211,192,233,226,320,234,184,206,219,199,212,191,187,188,189,190,186,368,354,378,333,355,336,367,335,334,337,43,29,324,0,35,57,15,50,8,22,44,24,325,23,2,30,58,16,51,9,45,25,322,18,3,31,59,17,52,10,46,26,329,19,4,32,54,12,53,11,47,27,328,20,5,33,55,13,48,6,42,28,21,323,1,34,56,14,49,7,41,37,38,39,40,36,351,377,376,330,332,353,366,331,352,365,164,144,301,122,150,178,136,171,129,143,165,145,300,138,123,151,179,137,172,130,166,146,302,139,124,152,174,132,173,131,167,147,303,140,125,153,175,133,168,126,162,148,304,141,120,154,176,134,169,127,163,149,142,305,121,155,177,135,170,128,156,158,159,160,161,157,364,362,349,350,363,374,375,347,379,348,284,264,312,240,272,294,252,292,248,262,285,265,314,263,242,273,295,257,293,249,286,266,316,258,243,274,296,256,288,250,287,267,307,259,244,275,297,254,289,251,282,268,308,260,245,270,298,255,290,247,283,269,261,310,241,271,299,253,291,246,279,281,276,277,278,280,356,358,369,339,370,357,338,341,340,342 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#c539940867c986a0a1073206aa606fb301b27139c3e9357da4da5988ddbec2ae, 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 23:43:21 · history