Equation 677 Database

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Magma a752ece8a3b2…

magma a752ece8a3b2
Size
381
Isomorphism class hash
a752ece8a3b2df3d4d17acbb20495463462db62414254a23d2a1fc7e51f97360
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 23:27:01
Display reorder
380,285,280,291,297,272,275,192,197,202,207,182,187,157,162,167,172,177,152,119,114,115,116,117,118,301,300,302,303,304,305,104,105,106,107,102,103,99,100,101,96,97,98,242,247,252,257,262,267,108,109,110,111,112,113,222,227,232,237,212,217,95,94,90,91,92,93,334,354,344,349,362,365,372,357,377,348,289,284,293,299,274,279,194,199,204,209,184,189,159,164,169,174,179,154,143,138,139,140,141,142,319,321,322,324,326,328,128,129,130,131,126,127,123,124,125,120,121,122,244,249,254,259,264,269,132,133,134,135,136,137,224,229,234,239,214,219,145,144,146,147,148,149,339,353,345,346,364,369,374,361,379,331,286,281,294,296,271,276,190,195,201,206,180,185,156,161,166,170,175,151,3,4,5,1,0,2,317,312,313,314,315,316,18,19,20,21,22,23,12,13,14,15,16,17,240,245,251,256,261,266,28,29,24,25,26,27,220,225,231,236,210,215,9,8,10,11,6,7,340,351,333,332,355,367,371,358,375,336,287,282,290,295,270,277,191,196,200,205,181,186,155,160,165,171,176,150,78,79,80,81,82,83,318,320,323,325,327,329,67,68,69,70,71,66,64,65,60,61,62,63,241,246,250,255,260,265,77,72,73,74,75,76,221,226,230,235,211,216,89,88,84,85,86,87,337,350,338,343,359,368,370,360,376,335,288,283,292,298,273,278,193,198,203,208,183,188,158,163,168,173,178,153,54,55,56,57,58,59,309,310,311,306,307,308,43,44,45,46,47,42,40,41,36,37,38,39,243,248,253,258,263,268,53,48,49,50,51,52,223,228,233,238,213,218,34,33,35,30,31,32,330,352,342,341,363,366,373,356,378,347 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {74} 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 23:27:02 · history