Equation 677 Database

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Magma dafea568078c…

magma dafea568078c
Size
381
Isomorphism class hash
dafea568078c9926b4247e2c5a4083b9ee3bede12776d5fbac8ae8f002bbc604
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 23:29:02
Display reorder
380,93,88,83,27,223,26,138,143,148,123,128,132,268,273,278,283,288,298,243,248,238,258,263,253,321,322,323,318,319,320,218,25,24,78,68,73,98,103,228,113,118,108,63,58,213,54,44,48,178,168,173,163,153,158,29,233,28,293,30,31,184,189,194,199,204,209,334,338,353,363,343,358,349,368,378,373,91,86,81,1,221,0,137,142,147,122,127,131,267,272,277,280,285,295,240,245,236,257,260,250,328,329,327,325,326,324,215,4,5,76,65,71,95,100,226,110,115,106,60,56,210,51,41,45,177,167,172,162,152,157,10,230,11,291,8,9,180,185,190,196,201,206,331,336,351,362,340,355,346,367,377,372,92,87,82,19,222,18,135,140,145,121,126,134,265,270,275,282,286,296,241,247,237,255,261,251,300,302,301,304,305,303,217,16,17,77,67,72,97,102,227,112,117,107,62,57,212,53,43,47,175,165,170,161,151,156,21,232,20,292,22,23,183,188,193,198,203,208,333,337,352,360,342,357,347,366,376,371,94,89,84,37,224,36,139,144,149,124,129,133,269,274,279,284,289,299,244,249,239,259,264,254,311,309,310,308,306,307,219,38,39,79,69,74,99,104,229,114,119,109,64,59,214,50,40,49,179,169,174,164,154,159,33,234,32,294,34,35,181,186,191,195,200,205,330,339,354,364,344,359,348,369,379,374,90,85,80,7,220,6,136,141,146,120,125,130,266,271,276,281,287,297,242,246,235,256,262,252,316,317,315,313,314,312,216,3,2,75,66,70,96,101,225,111,116,105,61,55,211,52,42,46,176,166,171,160,150,155,12,231,15,290,13,14,182,187,192,197,202,207,332,335,350,361,341,356,345,365,375,370 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, 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 23:29:03 · history