Equation 677 Database

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Magma ab83e386a685…

magma ab83e386a685
Size
381
Isomorphism class hash
ab83e386a6855314e33091c17fa98a016cd55a120c75f2d334c5f004edcee1b2
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 23:47:33
Display reorder
380,206,234,302,219,233,192,226,191,212,199,207,235,200,303,220,228,193,227,186,213,236,208,201,304,221,229,194,222,187,214,237,209,202,305,216,230,195,223,188,215,204,238,203,301,217,231,196,224,189,210,198,239,205,300,218,232,197,225,190,211,183,185,180,181,182,184,371,372,345,344,362,361,363,364,370,373,176,120,312,134,148,162,141,161,127,169,177,121,170,313,135,149,163,142,156,128,122,178,171,314,136,144,164,143,157,129,123,179,172,315,137,145,165,138,158,130,174,124,173,310,132,146,166,139,159,131,168,125,175,311,133,147,167,140,160,126,153,155,150,151,152,154,335,350,351,334,333,331,367,352,332,330,44,23,318,2,16,30,9,58,24,37,45,18,38,319,3,17,31,10,59,25,19,46,39,320,4,12,32,11,54,26,20,47,40,321,5,13,33,6,55,27,42,21,41,316,1,14,34,7,56,28,36,22,43,317,0,15,35,8,57,29,50,52,53,48,49,51,375,348,346,379,376,349,365,374,366,347,267,295,306,280,288,253,287,246,273,260,268,296,261,323,281,289,254,282,247,274,297,269,262,324,276,290,255,283,248,275,298,264,263,326,277,291,256,284,249,270,265,299,258,329,278,292,257,285,250,271,259,294,266,309,279,293,252,286,251,272,244,240,241,242,243,245,354,336,378,337,358,357,377,353,356,355,112,85,322,70,78,98,77,91,63,105,113,86,106,325,71,79,99,72,92,64,87,108,107,327,66,80,100,73,93,65,88,109,102,328,67,81,101,74,94,60,110,89,103,307,68,82,96,75,95,61,104,84,111,308,69,83,97,76,90,62,118,114,115,116,117,119,368,339,343,360,342,359,369,338,341,340 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#e28c792184790f687caadc40055bb14fcba72e2bd9ede02943d40b210ab03e94, 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 23:47:34 · history