Equation 677 Database

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Magma 31a34f1911bd…

magma 31a34f1911bd
Size
381
Isomorphism class hash
31a34f1911bd8fcc295e78fd0aa9142f08b9943ef1f0b96a68eb64317fc7da54
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 23:16:58
Display reorder
380,117,116,118,119,114,115,113,108,109,110,111,112,191,265,271,283,291,186,245,250,226,231,236,240,99,100,101,96,97,98,170,175,180,156,160,165,106,107,102,103,104,105,311,306,307,308,309,310,296,255,151,261,276,286,196,201,206,210,215,220,95,94,90,91,92,93,357,352,337,342,338,365,377,374,351,364,5,4,1,0,2,3,9,10,11,6,7,8,193,268,273,282,293,188,248,253,228,233,238,243,20,21,22,23,18,19,173,178,183,158,163,168,26,27,28,29,24,25,323,318,319,320,321,322,298,258,153,263,278,288,198,203,208,213,218,223,14,13,15,16,17,12,359,333,343,344,345,368,378,373,339,363,86,85,87,88,89,84,78,79,80,81,82,83,192,267,272,280,290,185,246,251,225,230,235,241,70,71,66,67,68,69,171,176,181,155,161,166,73,74,75,76,77,72,300,302,303,304,305,301,295,256,150,260,275,285,195,200,205,211,216,221,64,63,65,60,61,62,356,350,335,331,348,366,375,371,349,360,50,49,51,52,53,48,42,43,44,45,46,47,190,266,270,281,292,187,247,252,227,232,237,242,34,35,30,31,32,33,172,177,182,157,162,167,37,38,39,40,41,36,317,312,313,314,315,316,297,257,152,262,277,287,197,202,207,212,217,222,58,57,59,54,55,56,358,346,340,332,334,367,376,372,347,362,140,139,141,142,143,138,132,133,134,135,136,137,194,269,274,284,294,189,249,254,229,234,239,244,124,125,120,121,122,123,174,179,184,159,164,169,127,128,129,130,131,126,329,324,325,326,327,328,299,259,154,264,279,289,199,204,209,214,219,224,148,147,149,144,145,146,355,353,341,330,336,369,379,370,354,361 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {71} 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 23:16:59 · history