Equation 677 Database

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Magma 33c61139328f…

magma 33c61139328f
Size
381
Isomorphism class hash
33c61139328fad990c76753e896fe792abc7123d450c2e434c242a9685a4c322
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:36:26
Display reorder
380,103,170,119,153,118,102,152,150,104,151,305,128,195,144,178,143,301,175,127,177,129,176,3,220,19,203,18,300,202,2,201,4,200,28,245,44,228,43,302,226,27,29,227,225,53,270,69,253,68,303,52,251,252,54,250,78,295,94,278,93,304,277,276,77,79,275,336,359,337,361,335,360,373,330,356,349,107,163,105,165,100,108,171,154,106,166,326,132,188,130,190,125,327,179,133,196,131,191,7,213,5,215,0,328,221,8,204,6,216,32,238,30,240,25,329,229,33,31,246,241,57,263,55,265,50,324,58,254,271,56,266,82,288,80,290,75,325,296,279,83,81,291,339,364,338,362,340,363,374,331,355,332,109,155,112,158,111,110,169,168,101,159,309,134,180,137,183,136,310,193,135,194,126,184,9,205,12,208,11,311,219,10,218,1,209,34,230,37,233,36,306,243,35,26,244,234,59,255,62,258,61,307,60,268,269,51,259,84,280,87,283,86,308,294,293,85,76,284,333,365,334,358,341,357,367,342,366,343,115,160,113,162,117,116,157,167,114,172,317,140,185,138,187,142,312,192,141,182,139,197,15,210,13,212,17,313,207,16,217,14,222,40,235,38,237,42,314,242,41,39,232,247,65,260,63,262,67,315,66,267,257,64,272,90,285,88,287,92,316,282,292,91,89,297,346,371,345,369,347,370,368,348,372,344,124,174,122,173,121,120,161,164,123,156,321,149,199,147,198,146,322,189,145,186,148,181,24,224,22,223,21,323,211,20,214,23,206,49,249,47,248,46,318,239,45,48,236,231,74,274,72,273,71,319,70,264,261,73,256,99,299,97,298,96,320,286,289,95,98,281,354,375,353,378,350,379,377,351,376,352 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#970d88967a4a9e890c9bcd6ee64fc0a7382074eff0726754185bf13c51c510f8, 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 23:36:27 · history