Equation 677 Database

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Magma 59d45e3c9a2b…

magma 59d45e3c9a2b
Size
381
Isomorphism class hash
59d45e3c9a2bdd196d4ae5924ed157bed6c57659de3df88708f123f6b4ba0b13
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 23:38:49
Display reorder
380,215,64,63,61,62,60,221,4,5,280,68,69,272,277,285,257,262,267,122,127,132,137,142,147,152,157,162,167,172,177,292,101,96,112,117,106,313,314,312,316,317,315,59,56,55,58,213,57,27,28,29,252,25,26,240,245,296,226,231,236,197,207,202,192,182,187,338,362,367,346,355,332,352,377,372,340,216,8,9,10,11,65,220,66,67,281,13,12,270,276,286,256,261,266,123,128,133,138,143,148,153,158,163,168,173,178,290,102,97,110,116,105,304,305,303,300,302,301,31,32,30,34,210,33,51,49,50,250,52,53,241,246,299,225,230,235,198,208,203,193,183,188,335,363,366,345,356,333,350,375,373,341,219,91,90,24,92,23,224,7,6,284,93,94,274,279,289,259,264,269,120,126,131,135,141,145,150,156,161,165,171,175,294,104,99,114,119,108,327,328,329,324,325,326,41,44,40,43,212,42,37,35,36,254,38,39,244,249,298,229,234,239,195,205,200,191,180,186,337,360,369,349,359,330,354,379,370,344,217,76,75,0,77,1,222,2,3,282,78,79,271,275,287,255,260,265,124,129,134,139,144,149,154,159,164,169,174,179,291,100,95,111,115,107,307,308,306,310,311,309,70,71,72,73,214,74,46,47,48,251,45,54,242,247,295,227,232,237,199,209,204,194,184,189,339,364,365,347,357,334,351,376,374,342,218,81,80,19,82,20,223,21,22,283,83,84,273,278,288,258,263,268,121,125,130,136,140,146,151,155,160,166,170,176,293,103,98,113,118,109,318,319,320,321,322,323,16,17,18,14,211,15,86,87,85,253,89,88,243,248,297,228,233,238,196,206,201,190,181,185,336,361,368,348,358,331,353,378,371,343 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, 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 23:38:50 · history