Equation 677 Database

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Magma aa381e6e0fa1…

magma aa381e6e0fa1
Size
381
Isomorphism class hash
aa381e6e0fa1ab56bf96b5205010bb7b7744861a0012c0f4603c553a68f2a2f3
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 23:22:19
Display reorder
380,152,142,132,97,107,117,82,92,72,252,232,242,165,155,160,1,12,22,32,207,217,222,202,37,47,57,308,310,306,257,197,267,272,187,277,192,262,147,137,102,112,77,67,237,247,280,7,27,212,62,42,307,309,177,182,127,122,87,292,170,17,227,52,311,297,287,342,377,371,347,350,357,332,337,363,369,154,143,133,98,108,118,83,94,73,254,233,244,169,159,164,4,13,23,34,208,219,224,203,38,48,58,312,314,316,258,199,268,273,188,279,193,263,148,138,103,113,78,68,239,249,284,8,28,214,64,43,317,313,178,183,128,124,88,293,174,18,229,53,315,299,289,344,378,370,348,351,358,333,338,360,368,151,141,131,96,106,115,81,90,71,250,230,240,167,157,162,2,10,20,31,206,216,221,201,36,46,55,322,324,329,256,195,266,271,185,276,190,261,145,136,101,111,76,66,235,245,282,5,26,211,60,41,321,323,175,180,126,120,85,290,172,15,226,51,327,296,285,340,375,372,345,352,355,331,335,364,365,153,144,134,99,109,119,84,93,74,253,234,243,166,156,161,0,14,24,33,209,218,223,204,39,49,59,318,326,319,259,198,269,274,189,278,194,264,149,139,104,114,79,69,238,248,281,9,29,213,63,44,320,325,179,184,129,123,89,294,171,19,228,54,328,298,288,343,379,373,349,353,359,334,339,362,367,150,140,130,95,105,116,80,91,70,251,231,241,168,158,163,3,11,21,30,205,215,220,200,35,45,56,303,305,300,255,196,265,270,186,275,191,260,146,135,100,110,75,65,236,246,283,6,25,210,61,40,302,304,176,181,125,121,86,291,173,16,225,50,301,295,286,341,376,374,346,354,356,330,336,361,366 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {73} 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 23:22:22 · history