Equation 677 Database

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Magma 917022d4a1bb…

magma 917022d4a1bb
Size
381
Isomorphism class hash
917022d4a1bbbe7df9637d62078649516427ce4062855437595030c7d95c2200
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 23:16:29
Display reorder
380,91,100,305,118,113,109,95,105,96,114,92,115,101,306,119,111,110,93,106,97,90,116,99,307,117,112,108,94,107,98,88,61,79,66,74,83,308,70,65,75,76,62,89,80,67,72,81,309,71,63,77,87,60,78,68,73,82,310,69,64,86,84,102,103,104,85,354,356,378,336,364,379,355,357,377,363,240,260,318,294,283,278,248,270,253,288,242,289,258,319,295,284,276,247,271,252,241,290,259,317,296,282,277,246,272,254,275,279,255,293,244,261,321,297,286,251,249,280,273,256,291,245,262,322,298,287,250,274,281,257,292,243,263,320,299,285,267,268,266,264,265,269,338,359,365,340,337,330,375,366,339,358,222,231,315,221,213,212,226,239,230,217,223,218,232,316,219,214,210,227,237,228,224,216,233,314,220,215,211,225,238,229,191,192,182,200,205,183,312,201,196,209,207,193,189,180,198,206,184,313,202,197,208,190,194,181,199,204,185,311,203,195,186,187,236,234,235,188,373,352,362,351,350,353,371,372,374,370,27,8,324,26,18,17,1,13,4,22,28,23,6,325,24,19,15,0,14,5,29,21,7,323,25,20,16,2,12,3,30,34,52,39,47,56,327,43,38,48,49,35,31,53,40,45,54,328,44,36,50,32,33,51,41,46,55,326,42,37,59,57,10,11,9,58,345,332,360,343,367,344,342,376,341,331,171,152,300,170,162,161,175,157,179,166,172,167,150,302,168,163,159,176,158,177,173,165,151,301,169,164,160,174,156,178,140,141,131,149,123,132,304,122,145,127,128,142,138,129,147,124,133,329,120,146,126,139,143,130,148,125,134,303,121,144,135,136,154,155,153,137,333,348,349,347,361,368,334,335,346,369 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#096971eaef83bffb395a381c19275e6a285568ab61ce7a4c541144386a9bcf7a, 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 23:16:30 · history